- 1. These lessons are designed to be copied for the classroom,
with both a question and an answer page. If you have questions or
would like to submit lessons for future publication, contact
Microns K-12 Programs. Algebra Analysis and Probability Geometry
Measurements Numbers and Operations Accountant Accountant/CPA
Architect Area Sales Manager Assembly Operator Bank Teller Benefits
Manager BLM Operations Coordinator Bookkeeper Business Manager
Cardiovascular Specialist Carpenter Ceramic Tile Setter Chemist
Construction Contractor Construction Supervisor Container Supply
Dental Assistant Director International Finance Disk Drive Engineer
Electrical Contractor Math in the Workplace
2. Electrician Engineer - Semiconductor Equipment Engineer
Estimator Excavator Facility Representative - Utilities Family
Physician Farm Owner/Manager Financial Analyst Financial Manager
Financial Services - Vice President Food Broker Forest
Mensurationist Geologist Geologist (Mining) GIS Analyst Glass
Installer Graphic Designer Home Improvement: Concrete Home
Improvement: Remodeling Homemaker: Redecorator Homemaker:
Seamstress Lawn Mower Manufacturer Lead Estimator Licensed
Practical Nurse 3. Lumber Sales Rep Machine Operator Manager -
Government Agency Manager - Manufacturing Manager - Produce
Department Manager - Property Development Manager - R&D Program
Manager - Retail Store Manager - Telemarketing Manufacturing
Engineer Manufacturing Technician Medical Technologist Mortgage
Loan Officer Nutrition Specialist Office Manager/Bookkeeper
Operating Room Nurse Painter Pastor Payroll Clerk Process Engineer
Process Engineer - Cost Process Engineer - Design Physician Plumber
Police Officer 4. Production Planner Production Supervisor Property
Manager Purchasing Agent Quality Control Railroad Conductor Real
Estate Planner Realtor Registered Dietician Registered Nurse Road
Management Technician Sales / Adminstrative Assistant Salesperson -
Shoe Department Software Specialist Tax Analyst Tax Specialist
Teacher - Elementary Technical Writer Test Engineer Textile Screen
Printing Treasury Analyst Veterinarian - Equine Veterinarian -
Small Animal 5. Measurements: Road Management Technician Ada County
Highway District Job Description: Inspects pavement, calculates
asphalt estimates and reports inspection data to the ACHD
maintenance department. Problem: The Ada County Highway District
Pavement Management Technician needs to know how many tons of
asphalt will be needed on a section of road. The section of road
measures 5,280 feet (1 mile) in length and 26 feet wide. The
asphalt needs to be 3 inches in depth. Asphalt weighs 144 tons per
2,000 ft. 6. Measurements: Road Management Technician Ada County
Highway District Job Description: Inspects pavement, calculates
asphalt estimates and reports inspection data to the ACHD
maintenance department. Problem: The Ada County Highway District
Pavement Management Technician needs to know how many tons of
asphalt will be needed on a section of road. The section of road
measures 5,280 feet (1 mile) in length and 26 feet wide. The
asphalt needs to be 3 inches in depth. Asphalt weighs 144 tons per
2,000 ft. Solution: 3 inches x 12 inches = .25 ft or ft 144 tons
2000 ft = .072 tons of asphalt per cubic foot length x width x
depth x weight per ft = tons of asphalt 5,280 ft x 26 ft x .25 ft x
.072 tons = 2,471 tons of asphalt needed 7. Numbers and Operations:
Assistant Produce Manager Albertsons, Inc. Job Description: Oversee
the daily operation of the produce department for Albertsons
grocery store. Problem: Find the percent of gross profit on sales
of $100,000. The cost of the goods sold is $75,000. 8. Numbers and
Operations: Assistant Produce Manager Albertsons, Inc. Job
Description: Oversee the daily operation of the produce department
for Albertsons grocery store. Problem: Find the percent of gross
profit on sales of $100,000. The cost of the goods sold is $75,000.
Solution: Subtract the cost of the goods sold from the sales and
divide the sum by the sales. Sales 100,000 Cost - 75,000 25,000
25,000 100,000 = .25 Your percent of gross profit would be 25% on
the items you sold. 9. Numbers and Operations: Food Broker
Albertsons, Inc. Job Description: Brings the seller and the buyer
of food together. Problem: What is the retail price at Albertson's
grocery store of a package of Gallo Pepperoni? The case cost of the
pepperoni is $24 per 12 (8 oz.) packages. The warehouse markup will
be 7%. The store markup will be 38%. Store markup is on top of
warehouse markup. 10. Numbers and Operations: Food Broker
Albertsons, Inc. Job Description: Brings the seller and the buyer
of food together. Problem: What is the retail price at Albertson's
grocery store of a package of Gallo Pepperoni? The case cost of the
pepperoni is $24 per 12 (8 oz.) packages. The warehouse markup will
be 7%. The store markup will be 38%. Store markup is on top of
warehouse markup. Solution: Package cost = $24.00 12 packages =
$2.00/package Warehouse markup =$2.00 x .07 = $.14 Albertsons
markup =$2.14 (door cost) x .38 = $.81 Albertsons retail price
=$2.00 + .14 + .81 = $2.95/package 11. Numbers and Operations: Real
Estate Planner Albertsons, Inc. Job Description: Responsible for
day-to-day operations of commercial properties, provides lease
administration for the commercial portfolio, and participates in
budgeting and financial reporting to maximize financial returns.
Problem: A real estate manager has selected a location for a new
grocery store. How would Management determine the total cost of
project? The building will be 55,922 square feet at a building cost
of $50/sq. ft. The land purchase is 250,000 square feet at a cost
of $4.25/sq. ft. However, the company will only use 240,000 square
feet of the land (retained land) and the remaining amount will be
sold as surplus land at the same rate as purchased. Improvements to
the site (site costs) will be $1.25/sq. ft. 250,000 sq. ft. 55,922
sq. ft. 12. Numbers and Operations: Real Estate Planner Albertsons,
Inc. Job Description: Responsible for day-to-day operations of
commercial properties, provides lease administration for the
commercial portfolio, and participates in budgeting and financial
reporting to maximize financial returns. Problem: A real estate
manager has selected a location for a new grocery store. How would
Management determine the total cost of project? The building will
be 55,922 square feet at a building cost of $50/sq.ft. The land
purchase is 250,000 square feet at a cost of $4.25/sq. ft. However,
the company will only use 240,000 square feet of the land (retained
land) and the remaining amount will be sold as surplus land at the
same rate as purchased. Improvements to the site (site costs) will
be $1.25/sq. ft. Solution: Store Occupancy Costs Total Cost of
Retained Land (ft ): 240,000 x $4.25 =$1,020,000 Site Costs:
240,000 x $1.25 = $300,000 Building Costs: 55,922 x $50.00 =
$2,796,100 Total Building and Site Improvement Costs: 300,000 +
2,796,100 = $3,096,100 Total Cost of Project: 3,096,100 + 1,020,000
= $4,116,100 250,000 sq. ft. 55,922 sq. ft. 13. Analysis &
Probability/Algebra: Forest Mensurationist Boise Cascade
Corporation Job Description: Use mathematics and statistics to
inventory forest resources and predict the state of those resources
in the future. Problem: In forestry, we can describe the
relationship between the age of stand and the yield (timber volume)
in that stand with the following "yield equation": y = ke-bA , y =
yield, e is the base of natural logarithms, A = stand age, and k
and b are constants that depend on the type of stand (species,
geography, etc.) The yield equation can be used to draw a yield
curve, which looks like this: If the yield at any age is divided by
the age, we can derive the Mean Annual Increment (MAI), a measure
of the rate of growth for that stand up to that age. The age at
which MAI is maximized is known as the "rotation age", the age at
which the stand should be harvested, and then begin a new stand (a
new rotation). Here is the problem, which can be solved with
calculus: Find the age at which MAI is maximized or use the
definition of MAI to develop an expression for the rotation age.
[Hint: the yield equation shown above is popular because the
rotation age = b; so the rotation age can be read directly from the
yield equation] 14. Analysis & Probability/Algebra: Forest
Mensurationist Boise Cascade Corporation Job Description: Use
mathematics and statistics to inventory forest resources and
predict the state of those resources in the future. See problem for
details. Solution: Use calculus to show the age at which MAI is
maximized is equal to b. 15. Algebra: Treasury Analyst Boise
Cascade Forest Products Job Description: Has direct responsibility
for managing corporate short-term borrowings and investments.
Problem: The company has a debt payment due on May 1st in the
amount of $5,000,000. It currently has $5,000,000 available to meet
the obligation; but is not allowed to make the payment until the
due date, May 1st. The company would like to purchase an
investment, which at maturity would have a value equal to the
amount of the debt payment-thus allowing the excess cash to be used
elsewhere. Using the following assumptions, determine the price of
the required investment and the amount of excess cash they are
holding. Assumptions Debt payment required: $5,000,000 (P) Cash on
hand: $5,000,000 Interest rate (or discount rate) on investment: 6%
(IR) Days until debt payment date: 63 (DM) Dollar Price: amount
required to invest today to meet debt obligation in 63 days (DP) A
year consist of 360 days for interest accrual formula: P x (1 - (IR
x DM 360)) = DP 16. Algebra: Treasury Analyst Boise Cascade Forest
Products Job Description: Has direct responsibility for managing
corporate short-term borrowings and investments. Problem: The
company has a debt payment due on May 1st in the amount of
$5,000,000. It currently has $5,000,000 available to meet the
obligation; but is not allowed to make the payment until the due
date, May 1st. The company would like to purchase an investment,
which at maturity would have a value equal to the amount of the
debt payment-thus allowing the excess cash to be used elsewhere.
Using the following assumptions, determine the price of the
required investment and the amount of excess cash they are holding.
Assumptions Debt payment required: $5,000,000 (P) Cash on hand:
$5,000,000 Interest rate (or discount rate) on investment: 6% (IR)
Days until debt payment date: 63 (DM) Dollar Price: amount required
to invest today to meet debt obligation in 63 days (DP) A year
consists of 360 days for interest accrual formula: P x (1 - (IR x
DM 360)) = DP Solution: P x (1-(IR DM360)) = DP $5,000,000 x
(1-(.06 x 63 360)) = DP $5,000,000 x (1-(.0105)) = DP $5,000,000 x
(.9895) = DP $4,947,500 = DP Cash available for other purposes =
$52,500.00 ($5,000,000 - $4,947,500) Financial instruments such as
this one are referred to as "discounted" and include Banker's
Acceptances, Commercial Paper, Treasury Bills, and secondary
Discount Notes. 17. Numbers and Operations: Full Charge Bookkeeper
Boise Hardware, Inc. Job Description: Responsible for accounts
receivable, accounts payable, payroll, general ledger, inventory
maintenance. Problem: All employees have to have Federal Social
Security (FICA) and Medicare taxes taken from their gross wages.
Figure the FICA and Medicare taxes for the following employee's
gross wages and for the total gross wages. Gross wages is the total
earned before any deductions. FICA is 6.2% of the gross wages.
Medicare is 1.45% of the gross wages. employee a $ 540.00 employee
b $ 870.00 employee c $ 250.00 employee d $ 125.00 employee e
$1,600.00 18. Numbers and Operations: Full Charge Bookkeeper Boise
Hardware, Inc. Job Description: Responsible for accounts
receivable, accounts payable, payroll, general ledger, inventory
maintenance. Problem: All employees have to have Federal Social
Security (FICA) and Medicare taxes taken from their gross wages.
Figure the FICA and Medicare taxes for the following employee's
gross wages and for the total gross wages. Gross wages is the total
earned before any deductions. FICA is 6.2% of the gross wages.
Medicare is 1.45% of the gross wages. employee a $ 540.00 employee
b $ 870.00 employee c $ 250.00 employee d $ 125.00 employee e
$1,600.00 Solution: employee a $ 540.00 employee b $ 870.00
employee c $ 250.00 employee d $ 125.00 employee e +$1,600.00 Total
Gross Wages $3,385.00 FICA = 6.2% of $3,385 = $209.87 Medicare =
1.45% of $3,385 = $49.08 Employee FICA Medicare a 6.2% of $540 =
$33.48 1.45% of $540 = $7.83 b 6.2% of $870 = $53.94 1.45% of $870
= $12.62 c 6.2% of $250 = $15.50 1.45% of $250 = $3.63 d 6.2% of
$125 = $ 7.75 1.45% of $125 = $1.81 e 6.2% of $1600 = $99.20 1.45%
of $1600 = $23.20 Total $209.87 $49.09 19. Analysis &
Probability/Algebra: Cardiovascular Specialist Boise Heart Clinic
Job Description: Active cath lab and cardiovascular surgeon at the
hospitals and clinical physician of primary or secondary heart
disease at Boise Heart Clinic, P.A. Problem: #1 A man comes to the
hospital and needs a medication based on his body size. He weighs
170 lbs. The Doctor prescribes Dobutamine, which stimulates the
heart to increase the number of contractions and increases strength
of contraction of heart muscle to pump blood more effectively. He
needs to be given 10 mg/kg every minute of this medication
intravenously. If we put 500 mg of Dobutamine in one liter of
normal saline, how much solution do we need to give per hour? #2 A
59-year old man comes to the Boise Heart Clinic short of breath.
Dr. Lee hears a heart murmur and suspects the patient's aortic
valve is tight. He orders an echocardiogram (ultrasound of the
heart) to find the valve area of the aortic valve. If it is too
tight, he will have surgery to replace the valve. You must
calculate the aortic valve area: CSA = cross sectional area CSA=r
AVA = aortic valve area LVOT x CSA/AO LVOT = minimal flow (before
blood goes through the valve) AO = maximum flow (after blood goes
through the valve) = 3.14 LVOT = 1.0 m/sec AO = 5.8 m/sec LVOT
Diameter = 2.5 cm 20. Analysis & Probability/Algebra:
Cardiovascular Specialist Boise Heart Clinic Job Description:
Active cath lab and cardiovascular surgeon at the hospitals and
clinical physician of primary or secondary heart disease at Boise
Heart Clinic, P.A. See problem for details. Solution: #1 (Include
diagrams as needed) How much Dobutamine does this man need per min?
2.2 lbs = 1 kg 170 lbs 22 lb/kg = 77.3 kg 77.3 kg x (10 mg/kg)/min
= 773 mg/min How many liters per min? (1,000 ml 500 mg) x 773
mg/min = 155 ml/min = 1.55 liters/min How many liters per hour?
1.55 l/min x 60 min/hr = 93 l/hr #2 (Include diagrams as needed)
CSA = r = 3.14(2.5cm 2) = 4.9cm r = LVOT DIAM 2 AVA = LVOT x CSA AO
AVA = (1.0m/sec)(4.9cm) 5.8m/sec = .85 cm Aortic valve area ranges:
Normal - 2.6 cm to 1.6 cm Mild - 1.6 cm to 1.2 cm Moderate - 1.2 cm
to 1.0 cm Severe - 1.0 cm to 0.8 cm Critical - less than 0.75 cm
This patient has now been diagnosed with severe aortic stenosis. He
will have echocardiograms to monitor the tightness of the valve. He
will probably have a valve replacement in the near future. 21.
Numbers and Operations: Registered Dietitian Boise Heart Clinic Job
Description: Provide Medical Nutrition Therapy for hyperlipidemia
(high cholesterol and high triglycerides), hypertension, diabetes
and obesity to lower individual's risk of primary or secondary
heart disease. Problem: #1 Reading Food Labels This label came from
a can of soup (see label information at bottom of page). What are
percentages of calories from fat, saturated fat, total
carbohydrate, sugars, and protein? Saturated fats have the same
calories per gram as total fat. Sugars have the same calories per
gram as total carbohydrates. #2 Reading Food Labels If Americans
are encouraged to eat no more than 40% of their calories from total
fat, and no more than 10% of their calories from saturated fat, and
about 50% of their calories from total carbohydrates (not too high,
nor too low), how would you judge this product? 22. Numbers and
Operations: Registered Dietitian Boise Heart Clinic Job
Description: Provide Medical Nutrition Therapy for hyperlipidemia
(high cholesterol and high triglycerides), hypertension, diabetes
and obesity to lower individual's risk of primary or secondary
heart disease. See problem for details. Solution: #1 13 grams fat x
9 cal/gram = 117 fat calories 5 grams saturated fat x 9 cal/gram =
45 saturated fat calories 31 grams carbohydrates x 4 cal/gram = 124
carbohydrate calories 5 grams sugar x 4 cal/gram = 20 sugar
calories 5 grams protein x 4 cal/gram = 20 protein calories Percent
(%) of Calories from: 117 260 = 45% fat 45 260 = 17% saturated fat
124 260 = 48% carbohydrates 20 260 = 8% sugar 20 260 = 8% protein
#2 Goal Actual Rate =< 40% 45% total fat: very high "not at
goal" =< 10% 17% saturated fat: very high "not at goal" 50% 48%
total carbohydrates: good "at goal" 23. Analysis &
Probability/Algebra: Registered Dietitian Boise Heart Clinic Job
Description: Provide Medical Nutrition Therapy for hyperlipidemia
(highcholesterol and high triglycerides), hypertension, diabetes
and obesity to lower individual's risk of primary or secondary
heart disease. Problem: Leona is a 75-year-old woman with high
blood pressure, coronary artery disease, and adult-onset diabetes.
Lab values on 11-11-97 showed the following: LDL - 136 HDL - 28
Triglycerides - 326 Blood sugar - 239 Total cholesterol equals HDL
(high density lipids), plus LDL (low density lipids), plus VLDL
(very low density lipids), and VLDL equals 1/5 of Triglycerides.
Total Cholesterol = HDL + LDL + VLDL. 1. What are Leona's total
cholesterol level, VLDL levels and total cholesterol/HDL ratio?
(Round to the nearest tenth) The risk ratio for heart disease is a
ratio between the total cholesterol and HDL Levels. What is Leona's
risk ration? (Round to the nearest tenth) Circle her results as
desirable or high risk on the supplemental form. How likely is
Leona to have a heart attack? 24. Supplemental Form National
Cholesterol Education Program's Guidelines Desirable Borderline
High Total Cholesterol "DIET: low fat/high fiber" Less than 200
mg/dl 200-239 mg/dl 240 mg/dl or higher HDL Cholesterol (good
cholesterol) "DIET: weight loss/exercise" 45 mg/dl or higher 35-44
mg/dl Less than 35 mg/dl LDL Cholesterol (bad cholesterol) "DIET:
low fat/high fiber" No Coronary Heart Disease Less than 130 mg/dl
130-159 mg/dl 160 mg/dl or higher With Coronary Heart Disease Less
than 100 mg/dl 100-129 mg/dl 130 mg/dl or higher Triglycerides
"DIET: weight loss/exercise" Low refined sugars, low alcohol intake
Less than 165 mg/dl 165-249 mg/dl 250 mg/dl or higher Risk Ratio
(Total Cholesterol divided by HDL) Less than 4.5 4.5 More than 4.5
Fasting Glucose (Blood Sugar) "DIET: Weight control, exercise, low
refined sugars, balanced meal times" Less than 120 mg/dl 120-139
mg/dl 140 mg/dl or higher HDL, cholesterol, and your heart attack
risk Instructions: To help you track your progress and compare your
risk with others, plot your lipid levels on this graph after each
blood test. With a pencil, mark each axis at the points
corresponding to your high-density lipoprotein (HDL) and total
cholesterol levels. Then draw an imaginary line from each mark,
perpendicular to the axis, and mark the point on the chart where
both lines intersect. Write the date beneath the mark. 25. Your
triglyceride level is: 326 Chart your risk reduction over time DATE
HDL TOTAL TRIGS VISIT 1 11-11-97 28 229 326 VISIT 2 VISIT 3 VISIT 4
26. Analysis & Probability/Algebra: Registered Dietitian Boise
Heart Clinic Job Description: Provide Medical Nutrition Therapy for
hyperlipidemia (highcholesterol and high triglycerides),
hypertension, diabetes and obesity to lower individual's risk of
primary or secondary heart disease. See problem for details.
Solution: #1 (Use diagrams on supplemental form as needed)
Triglycerides VLDL = 326 5 = 65.2 VLDL VLDL + HDL + LDL = Total
Cholesterol 65.2 + 28 + 136 = 229 Formula: Total cholesterol HDL =
Risk ratio 229 28 = 8.2 ration #2 Leona has the lab values of
someone who just had a heart attack. Therefore, if she keeps these
values, Leona is VERY likely to have a heart attack. 27. Algebra:
Police Officer Boise Police Department Job Description: Traffic
investigation Problem: Background: A car travels 1.467 feet per
second for every 1 mph. The formula for speed at the start of skid
(in miles per hour) is S = f = coefficient of friction; d = skid
distance Total feet per second (fps) = miles per hour (mph) x 1.467
Total Stopping Distance = (reaction time) x (fps) + skid length
Time to impact = d v Questions: 1. Assuming a reaction time of .75
seconds, how fast was car A traveling at the beginning of its skid?
The coefficient of friction (f) on the road is .80. The coefficient
of friction is given for different circumstances, such as dry
pavement, snow floor, or black ice. 2. What was the total stopping
distance of car A? 3. How long did it take car B to turn if driver
A reacted immediately when car B began its turn? 28. Algebra:
Police Officer Boise Police Department Job Description: Traffic
investigation See problem page for details. Solution: 1. Speed at
the start of skid = Speed = 35 mph at the start of the skid 2.
Total stopping distance = reaction time x (speed at start of skid x
1.467) + skid length speed at start of skid = fps = 35 x 1.467 =
51.345 Total stopping distance = .75 x 51.345 ft + 50 foot skid =
88.5 ft Car A was 8889 feet from point of impact when car B started
the left turn. 3. Time = d v = Total stopping distance fps Time =
88.5 ft 51.345 = 1.7236 Time = 1.72 seconds for car B to begin
turning and get hit 29. Numbers and Operations: Operations
Coordinator Bureau of Land Management Job Description: Coordinates
logistical support for natural disasters and movement of incident
support resources. Problem: The company has been asked to help
fight a fire in the Phoenix, Arizona area. How much it will cost to
fly a Boeing 787 from the Boise Airport to Phoenix, Arizona to
assist in this fire fighting effort? Flight time to Phoenix is 1
hour and 47 minutes. Cost to fly one hour is $3,833. 30. Numbers
and Operations: Operations Coordinator Bureau of Land Management
Job Description: Coordinates logistical support for natural
disasters and movement of incident support resources. Problem: The
company has been asked to help fight a fire in the Phoenix, Arizona
area. How much it will cost to fly a Boeing 787 from the Boise
Airport to Phoenix, Arizona to assist in this fire fighting effort?
Flight time to Phoenix is 1 hour and 47 minutes. Cost to fly one
hour is $3,833. Solution: 1. Convert flight time in minutes to
hundredths of an hour. 47 minutes x 1 hour divided by 60 minutes =
0.78 hours + 1 hour = 1.78 hours or... 60 minutes + 47 minutes =
107 minutes 107 minutes x 1.6667 (convert minutes to hundredths) =
1.78 hours 2. Total flight time = 1.78 hr 1.78 hr x $3,833/hour =
$6,822.74 (cost to fly) 31. Analysis & Probability/Geometry:
Geologist (Mining) Bureau of Land Management Job Description:
Assessment of mineral resources, oversight of active mining
operations, geologic and mineral resource investigations. Problem:
Acme Mining Company is considering developing a small phosphate
mine in southeastern Idaho. The area has been explored, geology has
been mapped, and two drill holes (DH1 and DH2) were drilled. A
vertical, east-west oriented cross section of the area has been
drawn, as shown below. Note that the phosphate bed (a sedimentary
layer) is not flat, but is inclined. The angle of inclination from
a horizontal plane is known as the "dip" (d on the cross section).
The drill holes were drilled vertically and rock samples were
collected. The geologist on the drill rig recognized the change in
rock types as the hole was drilled downward. The following drill
data is given: Drill hole depth (feet) Rock type DH1 DH2 Surface,
alluvium 0 - 3' 0' - 3' Shale 3' - 75' 3' - 15' Phosphate 75' -
105' 15' - 42' Limestone 105' - 135' 42' - 80' Since mining is
expensive, it is important to the company to obtain an accurate
estimate of phosphate resources in this area to assess the economic
feasibility of developing a mine. If the resource is poor, the
costs of mining could well exceed the profits generated, thus the
company would go broke (and the geologist lose his or her job!). As
a first step in estimation of the volume and tonnage of resource,
the geologist needs to determine the average true thickness of the
phosphate bed. True thickness (t, on the cross section) is measured
perpendicular to the phosphate bed. Since the drill holes were
drilled vertically (at an angle to the inclined bed), the thickness
observed from the drill hole data is not true thickness, but is
"apparent" thickness. Assuming the ground level of DH1 is the same
level as the highest phosphate level of DH2, determine the dip
angle (d) and the average true thickness (t) of the phosphate bed
between the two drill holes. 32. Analysis &
Probability/Geometry: Geologist (Mining) Bureau of Land Management
Job Description: Assessment of mineral resources, oversight of
active mining operations, geologic and mineral resource
investigations. See problem for details. Solution: 1. Determine the
dip angle of bed (d) d = angle of true dip (inclination of bed from
horizontal) A right triangle is formed as shown, thus trigonometry
can be used to solve the problem. tan d = opposite/adjacent = 75
ft./ 150 ft. = .500 Using a calculator to determine angle: tan-1
26.6 2. Determine the true thickness (t) of phosphate bed (average
of "t" from PH1 + PH2). True thickness can also be calculated using
trigonometry. A right triangle is formed as shown. For DH1:
"Apparent" thickness from drill-data = 105' - 75' = 30' sin 63.4 =
opposite / hypotenuse = t / 30' t = 30sin 63.4 = 26.8 feet for t1
For DH2: "Apparent" thickness from drill-data = 42' - 15' = 27' sin
63.4 = t/27' t = 27 sin 63.4 = 24.1 feet for t2 3. Average
thickness = (26.8' + 24.1' ) / 2 25.5 feet Note: This problem could
also be solved graphically as an alternative. The result of 25.5
feet average thickness is significantly different from an average
of (30 +27)2 = 28.5 feet that would have been determined from
averaging the apparent thickness from drill-hole data. A difference
of 3 feet is significant when the volume of the entire resource
block is calculated. 33. Numbers and Operations: Office
Manager/Bookkeeper Computer Arts, Inc. Job Description: General
office operations including telephones, ordering supplies,
supervising employees, Accounts Receivable bookkeeping, Accounts
Payable, and payroll. Problem: Our company has a 401(K) Profit
Sharing Plan for employees. Employees may defer up to 15% of their
salary to the profit sharing plan. This is a great benefit to
employees. Not only is the deferral "pre-tax", the company offers a
"match" on the deferral. The 401(K) amount is deducted from the
gross payroll before Federal and State taxes are deducted. The
company matches $.50 on the dollar up to 3% of salary. Payment for
the deferrals and company match must be sent to the Trust each pay
period. The names of six employees, their monthly salary, and their
chosen deferral percentage are listed below. What is the total
check amount to the Trust each pay period? Complete the following
table: Employee Salary % Deferral Amount Match* Total Judy $1,000
15% Tom 1,200 10% Joe 2,000 3% Sue 900 5% Sally 1,500 3% John 1,750
7% 34. Numbers and Operations: Office Manager/Bookkeeper Computer
Arts, Inc. Job Description: General office operations including
telephones, ordering supplies, supervising employees, Accounts
Receivable bookkeeping, Accounts Payable, and payroll. See problem
page for details. Solution: Deferral Amount = Salary x % Deferral
Match* =Salary x 3% = Salary x 0.03 Example: Judy invests 15%,
which is $1000 x .15 = $150/month. The company matches $.50 on the
dollar up to 3%, which is $1000 x 0.03 = $30 x .50 = $15. The
company will add $15/month to Judy's investment. Total = Deferral
amount plus match amount. For Judy that is $150 + $15 = $165.
Employee Payroll % Deferral Amount Match* Total Judy $1,000 15%
$150.00 $15.00 $165.00 Tom 1,200 10% 120.00 18.00 138.00 Joe 2,000
3% 60.00 30.00 90.00 Sue 900 5% 45.00 13.50 58.50 Sally 1,500 3%
45.00 22.50 67.50 John 1,750 7% 122.50 26.25 148.75 Total check to
trust: $667.75 35. Numbers and Operations: Container Supply
Container & Packaging Supply, Inc. Job Description: Figures
costs, selling prices, manage employees, purchase equipment,
arrange for long-term financing and make decisions for the
direction of the company. Problem: I buy a product that costs me
$10.00. I need to make a 20% gross profit (selling price cost of
goods sold). What should my selling price be? What will my gross
profit be? 36. Numbers and Operations: Container Supply Container
& Packaging Supply, Inc. Job Description: Figures costs,
selling prices, manage employees, purchase equipment, arrange for
long-term financing and make decisions for the direction of the
company. Problem: I buy a product that costs me $10.00. I need to
make a 20% gross profit (selling price cost of goods sold). What
should my selling price be? What will my gross profit be? Solution:
Selling price (100%) Cost of Goods (80%) = Gross Profit (20%) To
calculate my selling price (x): x - $10 = (.20) x - .2x = $10 .8x =
$10 x = $10 .8 = $12.50 $12.50 - $10.00 = $2.50 gross profit 37.
Numbers and Operations: Assembly Operator Coretronics, Inc. Job
Description: Order and maintain sufficient parts to complete
customer orders. Assemble and test print heads. Problem: I buy a
product that costs me $10.00. I need to make a 20% gross profit
(selling price cost of goods sold). What should my selling price
be? What will my gross profit be? 38. Numbers and Operations:
Assembly Operator Coretronics, Inc. Job Description: Order and
maintain sufficient parts to complete customer orders. Assemble and
test print heads. Problem: I buy a product that costs me $10.00. I
need to make a 20% gross profit (selling price cost of goods sold).
What should my selling price be? What will my gross profit be?
Solution: 1. 173 hammers in supply 6 hammers per print head = 28.83
print heads Therefore, 28 print heads can be built with the hammers
currently stocked. 2. 45 print heads x 6 hammers per print head =
270 total hammers needed for entire order. 270 total hammers needed
- 173 hammers in supply = 97 hammers needed to complete the order.
This is an actual interview question. About 40% of applicants get
it right. 39. Numbers and Operations: Machine Operator Coretronics,
Inc. Job Description: Grind print heads using surface grinders.
Must know Imperial (U.S.) system to Metric system conversion.
Problem: Upon measuring the part you are machining, your inspection
tool says that an additional 0.45 mm needs to be removed. The
machine you are using only has controls calibrated in inches. (25.4
mm = 1 inch) How many inches do you need to remove from the part?
Do not use a calculator. Answer is to be given with 4 decimal
places. 40. Numbers and Operations: Machine Operator Coretronics,
Inc. Job Description: Grind print heads using surface grinders. .
Must know Imperial (U.S.) system to Metric system conversion.
Problem: Upon measuring the part you are machining, your inspection
tool says that an additional 0.45 mm needs to be removed. The
machine you are using only has controls calibrated in inches. (25.4
mm = 1 inch) How many inches do you need to remove from the part?
Do not use a calculator. Answer is to be given with 4 decimal
places. Solution: 0.45 mm x (1 inch 25.4 mm) = 0.45 inches / mm
25.4 mm = 0.0177 inches This is an actual interview question used.
About 40% of applicants get it right. 41. Algebra: Production
Planner Darigold Inc. Job Description: Plan ice cream production
and supervise employees Problem: How much ice cream mix and vanilla
flavor will it take to make 1000 gallons of vanilla ice cream at
90% overrun with the vanilla flavor usage rate at 1 oz. per 10
gallon mix? (90% overrun means that enough air is put into the
frozen mix to increase its volume by 90%). Note: 1 gallon = 128
fluid oz. 42. Algebra: Production Planner Darigold Inc. Job
Description: Plan ice cream production and supervise employees
Problem: How much ice cream mix and vanilla flavor will it take to
make 1000 gallons of vanilla ice cream at 90% overrun with the
vanilla flavor usage rate at 1 oz. per 10 gallon mix? (90% overrun
means that enough air is put into the frozen mix to increase its
volume by 90%). Note: 1 gallon = 128 fluid oz. Solution: Total
volume required = 1000 gal (1 + 0.9) = 526.3 gal Now let x = volume
of ice cream mix y = volume of vanilla flavor So x + y = 526.3 but
y = (0.00078)(x) - which is negligible So x = 526.3 But since we
need 1 oz. of flavoring for 10 gal of mix We get y oz 526.3 gal = 1
oz 10 gal Y = 52.6 oz of flavor 43. Measurements: Ceramic Tile
Setter Davis Tile Job Description: Installs ceramic tile. Problem:
Find the total square footage in the countertop illustrated. A = 2'
B = 11' C = 3' D = 6' 44. Measurements: Ceramic Tile Setter Davis
Tile Job Description: Installs ceramic tile. Problem: Find the
total square footage in the countertop illustrated. A = 2' B = 11'
C = 3' D = 6' Solution: A x (B + A) = E 2 x 13 = 26 ft2 A x A = F 2
x 2 = 4 ft2 A x C = G 2 x 3 = 6 ft2 C x D = H 3 x 6 = 18 ft2 E + F
+ G + H = Total area of countertop = 54 ft2 45. Geometry: Computer
Manufacturer Electrician Electrical Company Problem: When an
electrician wires a house, the switch boxes must be properly sized.
Each insulated wire (wire size called #14) requires 2.25 cubic
inches of space. Any number of bare wires all together only needs
another 2.25 cubic inches of space. Each cable contains two (2)
insulated and one (1) bare wire. How many cables can be put into a
box that is 3 inches deep? 46. Geometry: Computer Manufacturer
Electrician Electrical Company Problem: When an electrician wires a
house, the switch boxes must be properly sized. Each insulated wire
(wire size called #14) requires 2.25 cubic inches of space. Any
number of bare wires all together only needs another 2.25 cubic
inches of space. Each cable contains two (2) insulated and one (1)
bare wire. How many cables can be put into a box that is 3 inches
deep? Solution: Box volume is 3" x 3.5" x 2" or 21 in3 Space needed
for insulated wires: 21 in3 - 2.25 in3 = 18.75 in3 (all bare wires
need only 2.25 in3 ). Space needed for each cable that contains two
insulated wires: 2.25 in3 x 2 = 4.50 in3 Maximum number of cables
allowed: 18.75 in3 4.50 in3 = 4.166 Therefore, 4 cables can be put
into the box. 47. Measurements: Homemaker Redecorate Elizabeth
Crandlemire Job Description: Handyman, carpenter, plumber,
seamstress, cook, maintenance, engineer, mother, etc. Problem: I
want to wallpaper a 10' x 12' room that has 8' ceilings. The
wallpaper has 44 sq. ft. per double roll. How many double rolls of
wallpaper do I need to order? (Wallpaper is not available in single
rolls.) 48. Measurements: Homemaker Redecorate Elizabeth
Crandlemire Job Description: Handyman, carpenter, plumber,
seamstress, cook, maintenance, engineer, mother, etc. Problem: I
want to wallpaper a 10' x 12' room that has 8' ceilings. The
wallpaper has 44 sq. ft. per double roll. How many double rolls of
wallpaper do I need to order? (Wallpaper is not available in single
rolls.) Solution: Width x Height square footage = # of double rolls
needed 44 ft x 8 feet 44 sq ft/roll = 8 rolls ...OR add the area of
each wall [2 (10 x 8) + 2 (12 x 8) ] = 352 square feet 352 sq ft 44
sq ft/roll = 8 double rolls 49. Numbers and Operations:
Veterinarian Equine Hospital and Lameness Center Job Description:
Veterinary medicine and surgery. Problem: A horse weighs 1,200
pounds. He is sick and has been diagnosed with a certain disease.
This disease is treated with Drug X. Instructions are to give 3
mg/kg orally twice a day for 5 days. The medicine is provided in
200 mg tablets. 2.2 pounds = 1 kg How many tablets need to be
dispensed each day? How many tablets need to be dispensed for the 5
days of treatment? 50. Numbers and Operations: Veterinarian Equine
Hospital and Lameness Center Job Description: Veterinary medicine
and surgery. Problem: A horse weighs 1,200 pounds. He is sick and
has been diagnosed with a certain disease. This disease is treated
with Drug X. Instructions are to give 3 mg/kg orally twice a day
for 5 days. The medicine is provided in 200 mg tablets. 2.2 pounds
= 1 kg How many tablets need to be dispensed each day? How many
tablets need to be dispensed for the 5 days of treatment? Solution:
1,200 lbs 2.2 lbs/kg = 545 kgs (weight of horse) 545 kgs x 3 mg/kg
= 1,635 mg 1,635 mg x 2 times/day = 3,270 mg per day 3,270 mg/day
200 mg/pill = 16.35 or 16 pills per day 16.35 pills/day x 5 days =
81.75 pills to be dispensed Open-ended discussion: What would you
do about the partial pill? 51. Numbers and Operations: Retail Store
Manager Fred Meyer Job Description: Retail store operations
including pricing control, inventory control, employee supervision,
customer service and loss prevention. Budgeting and scheduling are
also common duties. Problem: 1. In a retail store, the profit on a
product is calculated as a percent of the retail price to the
customer. This is called margin. If the store pays $8.00 for a
music CD and wants to make a 20% margin, what would the retail
sales price need to be? 2. Margin differs from markup. Markup is
the percentage of profit based on the cost of the item while margin
is based on the sales price of the item. If the store pays $8.00
for a music CD and wishes a 20% markup, what would the sale price
be? Generally speaking, businesses use the margin method to
calculate the sales prices of their merchandise. 52. Numbers and
Operations: Retail Store Manager Fred Meyer Job Description: Retail
store operations including pricing control, inventory control,
employee supervision, customer service and loss prevention.
Budgeting and scheduling are also common duties. Problem: 1. In a
retail store, the profit on a product is calculated as a percent of
the retail price to the customer. This is called margin. If the
store pays $8.00 for a music CD and wants to make a 20% margin,
what would the retail sales price need to be? 2. Margin differs
from markup. Markup is the percentage of profit based on the cost
of the item while margin is based on the sales price of the item.
If the store pays $8.00 for a music CD and wishes a 20% markup,
what would the sale price be? Generally speaking, businesses use
the margin method to calculate the sales prices of their
merchandise. Solution: 1. Retail price with a 20% margin: Divide
the cost of the CD by 100% less the margin (20%) $8.00 /(100% -
20%) = $8.00/.80 = $10.00 retail sales price 2. Retail price with a
20% markup: Multiply the cost of the CD by 100% plus the markup
(20%) $8.00 x (100% + 20%) = $8.00 x 1.2 = $9.60 retail sales price
53. Numbers and Operations: Church Pastor Grace Bible Church of
Boise Job Description: Preach and teach the Bible; care for
people's spiritual needs through training and counseling; perform
weddings, funerals and other church services; train younger men to
become pastors. Problem: 1. In 1995, Grace Bible Church had 400
people attending. Forty of those people left to help start Nampa
Bible Church. Two years later, Grace Bible Church had 520 people,
and Nampa Bible Church had 200. a. What is the percentage of growth
for Grace Bible Church in the two years 1995 - 1997? b. What is the
percentage of growth for Nampa Bible Church in the two years 1995 -
1997? c. What is the combined growth for the two churches in the
two years 1995 - 1997? 2. If Grace Bible Church wants to build a
building large enough for its congregation in the year 2000, how
many seats should it have? 54. Numbers and Operations: Church
Pastor Grace Bible Church of Boise Job Description: Preach and
teach the Bible; care for people's spiritual needs through training
and counseling; perform weddings, funerals and other church
services; train younger men to become pastors. Problem: 1. In 1995,
Grace Bible Church had 400 people attending. Forty of those people
left to help start Nampa Bible Church. Two years later, Grace Bible
Church had 520 people, and Nampa Bible Church had 200. a. What is
the percentage of growth for Grace Bible Church in the two years
1995 - 1997? b. What is the percentage of growth for Nampa Bible
Church in the two years 1995 - 1997? c. What is the combined growth
for the two churches in the two years 1995 - 1997? 2. If Grace
Bible Church wants to build a building large enough for its
congregation in the year 2000, how many seats should it have?
Solution: 1: The percent of growth a. 520 - 400 / 400 = 120/400 =
.3 = 30% growth for Grace Bible Church. b. 200 - 40/40 = 160/40 =
4.0 = 400% growth for Nampa Bible Church. c. 720 - 400/400 =
320/400 = .8 = 80% combined growth 2: Seating anticipated in the
year 2000: Two years growth = 30% What is 3 years growth 1997-2000?
Estimate 1 year growth = 30% / 2 = 15% Three years growth = 15% x 3
= 45% 520 + 520(.45) = 520 + 234 = 754 55. Numbers and Operations:
HP Business Manager Hewlett Packard Job Description: Responsible
for business operations planning. Problem: We often travel from the
United States to Japan for business. As such, we need to convert US
Dollars to Japanese Yen for any business transaction. If a certain
item cost 150,000 yen (), how much would it be in US Dollars?
Assume an exchange rate of 115 to $1. 56. Numbers and Operations:
HP Business Manager Hewlett Packard Job Description: Responsible
for business operations planning. Problem: We often travel from the
United States to Japan for business. As such, we need to convert US
Dollars to Japanese Yen for any business transaction. If a certain
item cost 150,000 yen (), how much would it be in US Dollars?
Assume an exchange rate of 115 to $1. Solution: 150,000 115 = about
$1,304 57. Analysis & Probability/Algebra: Disk Drive Engineer
Hewlett-Packard Company Job Description: Design digital magnetic
recording systems for use in hard disk drives. Problem: A magnetic
recording engineer wants to determine the minimum write current
(Iw) he can use to drive a head to write magnetic transitions (bits
of information) onto a disk in a disk drive. The head cannot get
any closer than 25 nanometers (1 nanometer = 1 x 10-9 meters) to
the surface of the disk. The magnetic field at the head gap (Hg) is
roughly equal to product of the number of windings on the head (N)
times the write current (expressed in amps), divided by the
distance of the gap (G). Hg = (N x Iw) G The magnetic field is
expressed in a couple of terms, Oersteds (Oe) and AmpTurns/Meters.
One Orested is equal to 80AmpTurns/Meter. The head has 48 turns (or
windings,N) and the gap distance,G, is 1 micrometer (1 x 10-6
meters or 1 m). From previous modeling, he knows that the magnetic
field decreases with distance away from the gap, such that it is
roughly one half of Hg when the head is 25 nanometers away from the
disk. He knows there is a demagnetizing field (Hd) that occurs
inside the disk during the write process. This field opposes the
field from the head. Previous calculations showed that Hd is 500
Oersteds. The net field for writing (Hx) must be greater than the
coercivity (Hc) of the media plus the demagnetizing field. The
coercivity of the media has been measured at 2000 Oersteds. What is
the minimum write current? 58. Analysis & Probability/Algebra:
Disk Drive Engineer Hewlett-Packard Company Job Description: Design
digital magnetic recording systems for use in hard disk drives. See
problem for details. Solution: Hx > Hc + Hd Hx = net field for
writing Hc = coercivity of media Hd = Demagnetizing field Hc + Hd =
2000 Oe + 500 Oe = 2500 Oe Hx = 0.5 Hg Therefore, Hg = 2 Hx >
5000 Oe 1 Oe = 80 Amp Turns / Meter, abbreviated (A T) / m
Therefore, Hg > 5000 Oe (80 ) (A T)/m Hg > 1.26 106 A T/m Hg
= (Iw N)/G Iw = Hg G/N = (1.26 106 A T/m)(1 10-6 m) / 48 T Iw >
0.026 Amps or 26 10-3 Amps (26 milliamps) 59. Analysis &
Probability/Algebra: R&D Program Manager Hewlett-Packard
Company Job Description: Develop full business models for
development programs and work with all functional areas (R&D,
marketing, finance, manufacturing, etc.) to bring new products to
market. Problem: A new technology computer storage tape format has
been designed by a computer company. Other companies "license" the
right to produce products that use this format. They pay an initial
fee of $10,000 and then pay $10 for every tape cartridge sold. The
original company has expenses to develop, document and test this
new tape format. It wants to know if the new tape license format
will make money for the company. Given the following information .
. . Original company expenses: $1,000,000 to develop format. 1st
year expenses to set up documents and tests - $200,000. Each year
after 1st - $50,000 / year to maintain. Assume 5 companies license
the format: 2 during the 1st year and 3 more during the 2nd year.
Assume each new company will sell 5,000 tape cartridges the 1st
year and 10,000 tape cartridges every year after the 1st.
Questions: 1. How many years before the original development
company begins to earn money on its $1,000,000 R&D investment?
2. How much money does the original company make per year in the
year three after the "market is mature?" 3. Do you think this
investment was a good investment? 4. Which would affect the
decision most? a. what if initial license fee was $5,000 instead of
$10,000? b. what if more than 5 companies entered the market? c.
what if a new format "captured the market" in 4 years? 60. Analysis
& Probability/Algebra: R&D Program Manager Hewlett-Packard
Company Job Description: Develop full business models for
development programs and work with all functional areas (R&D,
marketing, finance, manufacturing, etc.) to bring new products to
market. Solution: (See problem for details.) 1. During which year
will the original development earn money, disregarding the
$1,000,000 R&D investment? Use a chart to organize income vs
expenses: Before Year 1 Year 1 Year 2 Year 3 Year 4 Expenses
$-1,000,000 $ -200,000 $ -50,000 $ -50,000 $ -50,000 License Fees
$20,000 (2$10,000) $30,000 (3$10,000) - 0 - - 0 - Income Per Tape
Fees $100,000 (2105,000) $200,000 (21010,000) $150,000 (3105,000)
$500,000 (51010,000) $500,000 (51010,000) Yearly Income $120,000
$380,000 $500,000 $500,000 Yearly Gain/Loss $-80,000 $330,000
$450,000 $450,000 Answer: During Year 2, the company begins to earn
more than it spends. Yearly Income - Yearly Expense = Yearly Gain
or Loss (Earnings) ($380,000 - $50,000 = $250,000) 2. After "market
is mature" no new companies buying a license, and all companies are
at final volume. [ (# of license companies) x (tape cartridges per
year) x ($ fee/cartridge) ] - expenses by original company [(5) x
($10,000) x ($10)] - $50,000 = $450,000 3. Was this a good
investment? Yes. By the end of Year 4, the original company has
regained its investment plus $150,000 and adds another $450,000 per
year. 4. Effects of "variation" - sensitivity analysis. a. License
only $5,000 only drops by $25,000 / minor change b. More than 5
license companies adds $100,000/year at "maturity" / major change
c. New format "captures market" in 4 years might make investment a
bad decision / difficult change 61. Numbers and Operations: IT
Software Specialist Hewlett Packard Job Description: Provide
operating system support and consulting to our worldwide customers.
Problem: Our data center has a total of 65 computers. Each quarter
we need to report to our customers the percentage of uptime for the
data center. If we are reporting for the months August, September,
and October and there are 49 computers that are up 100% of the
time, what is the percentage of computers available 100%. If the
total downtime of all 65 computers totals 2,435 minutes, what is
the average downtime per computer per month? What is the total
uptime percentage? 62. Numbers and Operations: IT Software
Specialist Hewlett Packard Job Description: Provide operating
system support and consulting to our worldwide customers. Problem:
Our data center has a total of 65 computers. Each quarter we need
to report to our customers the percentage of uptime for the data
center. If we are reporting for the months August, September, and
October and there are 49 computers that are up 100% of the time,
what is the percentage of computers available 100%. If the total
downtime of all 65 computers totals 2,435 minutes, what is the
average downtime per computer per month? What is the total uptime
percentage? Solution: (49 65) = 0.7538 x 100 = 75.38% computers
available 100% (2435 65) 3 = 12.49 min. average downtime/computers
per month (60 min. x 24 hrs.) = total minutes in a day = 1440
minutes (31 days + 30 days + 31 days) = total days in 3 months = 92
days 1440 x 92 x 65 = 8,611,200 total possible computing minutes
8,611,200 - 2,435 = 8,608,765 total actual computing minutes
(8,608,765 8,611,200) = .9997 x 100 = 99.97% uptime 63.
Measurements/Geometry: Handyman Concrete Home Improvement &
Repairs Job Description: Manage individuals who market, sell, and
support products that are currently on market (the problem is
submitted as a homeowner). Problem: A man needs to make a cement
driveway from his garage to the streeta distance of 135 feet. The
driveway needs to be 4 inches thick. Cement costs $55/cubic yard
with a 15% discount for cash. How many cubic yards of cement will
he need for a driveway with a width of 15 feet? How much will he
pay if he uses cash? 64. Measurements/Geometry: Handyman Concrete
Home Improvement & Repairs Job Description: Manage individuals
who market, sell, and support products that are currently on market
(the problem is submitted as a homeowner). Problem: A man needs to
make a cement driveway from his garage to the streeta distance of
135 feet. The driveway needs to be 4 inches thick. Cement costs
$55/cubic yard with a 15% discount for cash. How many cubic yards
of cement will he need for a driveway with a width of 15 feet? How
much will he pay if he uses cash? Solution: 1 cubic yard = 27 cubic
feet 4 inches = 4/12 foot Volume of driveway: 135 ft. x 15 ft. x
4/12 ft. = 675 cu. ft. 675 cu. ft. 27 cu. ft.= 25 cu. yd. 25
cu.yds. x $55/cu. yd. = $1,375 If bill is paid in cash, take 15% of
$1,375. Deduct $206.25 from the cost and customer. 65.
Measurements/Geometry: Handyman Remodeling Home Improvement &
Repair Job Description: Provide cost estimates to customers for
home projects. Problem: The cost of carpet is $13.00/square yard
and the cost to install the carpet is $5.00/square yard. The cost
of hardwood flooring is $7.00/square foot and the installation cost
is $2.00/square foot. Jon's family room measures 18 feet x 24 feet.
1) What is the cost for carpet, including installation? 2) What is
the cost for hardwood flooring, including installation? 3) What is
the total cost for hardwood, including installation, around a
perimeter four feet wide; and carpet, including installation, in
the remaining middle area of the family room floor? 66.
Measurements/Geometry: Handyman Remodeling Home Improvement &
Repair Job Description: Provide cost estimates to customers for
home projects. See problem page for details. Solution: 1. What is
the cost for carpet, including installation? carpet = $13/sq. yd.
Installation = $5/sq .yd. hardwood = $7/sq. ft. installation =
$2/sq. ft. 24 ft. x 18 ft. = 432 sq. ft of carpet needed $13
(carpet) + $5 (installation) = $18/sq .yd. installed carpet 432 sq.
ft. / 9 sq. ft. = 48 sq x $18/sq .yd. = $864 for carpet 2. What is
the cost of hardwood flooring including installation? 432 sq. ft. x
$9/sq. ft. = $3,888 for hardwood floor 3. What is the total cost
for the hardwood and carpet as described. (hardwood with carpet)
carpet = $13/sq .yd. installation = $5/sq .yd. hardwood = $7/sq.
ft. installation = $2/sq. ft. (24 ft. x 18 ft.) - (16 ft. x 10 ft.)
= 272 sq. ft. of hardwood needed $7 (hardwood) + $2 (installation)
= $9/sq .yd. installed hardwood 272 sq. ft. x $9/sq. ft. = $2,448
for hardwood (16 ft. x 10 ft.) / 9 sq. ft. = 17.77 sq .yd. of
carpet needed 17.77 sq .yd. x $18/sq .yd. = $320 for carpet $2,448
+ $320 = $2,768 total for hardwood and carpet 67. Geometry: Job
Estimator Idaho Barns Job Description: Sell and install
pre-fabricated barns and buildings. Price entire projects including
labor and materials. Problem: A family wants to buy a barn to keep
their animals in. The barn is 36 feet wide and 48 feet long. The
foundation requirements call for concrete pillars placed every 12
feet through the structure. The pillars are to be 2.5 feet deep and
12 inches in diameter. How much concrete will be used for this
project? The final amount needs to be calculated in cubic yards
because that is how concrete is sold. 68. Geometry: Job Estimator
Idaho Barns Job Description: Sell and install pre-fabricated barns
and buildings. Price entire projects including labor and materials.
Problem: A family wants to buy a barn to keep their animals in. The
barn is 36 feet wide and 48 feet long. The foundation requirements
call for concrete pillars placed every 12 feet through the
structure. The pillars are to be 2.5 feet deep and 12 inches in
diameter. How much concrete will be used for this project? The
final amount needs to be calculated in cubic yards because that is
how concrete is sold. Solution: 20 pillars are required for the
building. Calculate how much concrete is needed for each pillar and
multiply by 20. Circle area = r2 = 3.14 x 6 x 6 = 113.04 square
inches Cylinder volume = (r2 ) x ht 2.5 feet = 30 inches (113.04 sq
in) x (30 in) = 3391.2 cubic inches Convert to cubic feet 3391.2
cubic in 1,728 in3 /ft3 = 1.9625 cubic ft x 20 = 39.25 cubic feet
27 cubic feet = 1 cubic yard Convert to cubic yards 39.25 ft3 27ft3
/yd3 = 1.45 cubic yards of concrete needed 69. Geometry: Farm Owner
/ Manager Idaho Farm Owner Job Description:Operate farms, ranches,
greenhouses, nurseries, timber tracts, or other agricultural
production establishments which produce crops, horticultural
specialties, livestock, poultry, finfish, shellfish, or animal
specialties. May plant, cultivate, harvest, perform post-harvest
activities, and market crops and livestock; may hire, train, and
supervise farm workers or supervise a farm labor contractor; may
prepare cost, production, and other records. May maintain and
operate machinery and perform physical work. Problem: Betsy is
tethered to the barn at one corner by a 100 ft rope. A fence keeps
her out of the garden. Find, to the nearest square foot, the area
in which Betsy can graze. Area of triangle = base x height / 2 Area
of circle = r2 Area of sector = Area of circle x sector angle 360
70. Geometry: Farm Owner / Manager Idaho Farm Owner Job
Description: See problem page for details See problem for details.
Solution: Break the diagram into 4 different areas. Begin with
exact values and calculate the approximation at the end. 1. Area of
Section I is contained in a right isosceles triangle. Area of
Section I: (25 ft x 25 ft) 2 = 312.50 ft2 2. Area of Section II is
contained in a sector of a circle with a sector angle of 45, a
radius of 100 ft - diagonal of Section I isosceles triangle: 100 ft
ft = 100 ft - ft = 100 ft - 35.3553 ft = 64.6447 ft Area of Section
II: (64.6447 ft)2 360/45 = 13128.5 ft2 8 = 1,641.1 ft2 3. Area of
section III is contained in a sector of a circle with a sector
angle of 225 and a radius of 100 ft. Area of Section III: (100 ft)2
360/225 = 19,635 ft2 4. Area of Section IV is contained in a sector
of a circle with a sector angle of 90 and a radius of 100 ft - 80
ft = 20 ft. Area of Section IV: (20 ft)2 360 / 90 = 1,256.64 ft2 4
= 314.16 ft2 5. Area in which Betsy can graze = sum of areas of
Sections I - IV (312.50 + 1,641.1 + 19,635 + 314.16) ft2 = 21,903
ft2 71. Numbers and Operations: Bank Teller Idaho Independent Bank
Job Description: Help customers cash checks, make deposits, balance
different accounts and ledgers. Problem: A buyer wants to buy a
used car at a cost of $10,000.00 financed for 5 years or 60 months.
The buyer would like to know the savings on the finance charge if
he puts 10% down vs. 20% down against the loan at the time it is
taken out. Assumptions: The 60 monthly payments are: a. with 0%
down: $207.55 b. with 10% down: $186.80 c. with 20% down: $166.04
72. Numbers and Operations: Bank Teller Idaho Independent Bank Job
Description: Help customers cash checks, make deposits, balance
different accounts and ledgers. Problem: A buyer wants to buy a
used car at a cost of $10,000.00 financed for 5 years or 60 months.
The buyer would like to know the savings on the finance charge if
he puts 10% down vs. 20% down against the loan at the time it is
taken out. Assumptions: The 60 monthly payments are: a. with 0%
down: $207.55 b. with 10% down: $186.80 c. with 20% down: $166.04
Solution: Cost of Car % Down Original Loan Amount Payment x Months
= Total Total Loan Amount Finance Charge $10,000 0 % $10,000.00
$207.55 x 60 = $12,453.00 $12,453.00 $2,453.00 $10,000 10%
$9,000.00 $186.00 x 60 = $11,208.00 $11,208.00 $2,208.00 $10,000
20% $8,000.00 $166.04 x 60 = $ 9,962.40 $9,962.40 $1,962.40 1. By
putting 10% down at the time the loan is taken out, the buyer
saves: $2,453.00 - $2,208.00 = $245.00 2. By putting 20% down at
the time the loan is taken out, the buyer saves: $2,453.00 -
$1,962.40 = $490.60 73. Measurements: Physician Idaho Physical
Medicine & Rehabilitation Problem: You are the physician caring
for an 8 year old boy in the hospital. He weighs 62 pounds. You
need to calculate a flow rate for his IV fluids. You use the
following rule of thumb to determine the appropriate flow rate: 4
cc per hour per Kg for the first 10 Kg of bodyweight. (1 Kg = 2.2
pounds) Plus 2 cc per hour per Kg for the next 10 Kg of bodyweight
Plus 1 cc per hour per Kg for bodyweight over 20 Kg. How fast
should this boy's IV run in cc per hour? 74. Measurements:
Physician Idaho Physical Medicine & Rehabilitation Problem: You
are the physician caring for an 8 year old boy in the hospital. He
weighs 62 pounds. You need to calculate a flow rate for his IV
fluids. You use the following rule of thumb to determine the
appropriate flow rate: 4 cc per hour per Kg for the first 10 Kg of
bodyweight. (1 Kg = 2.2 pounds) Plus 2 cc per hour per Kg for the
next 10 Kg of bodyweight Plus 1 cc per hour per Kg for bodyweight
over 20 Kg. How fast should this boy's IV run in cc per hour?
Solution: Convert 62 pounds to Kg. 62 lbs. 2.2 lbs./Kg = 28 Kg
First 10 Kg: @ 4cc/hKg = 40 cc/h Second 10 Kg: @ 2cc/hKg = 20 cc/h
Final 8 Kg: @ 1cc/hKg = 8 cc/h Answer: 68 cc/h 75. Numbers and
Operations: Family Physician Idaho Physicians Associates Job
Description: Educate patients on wellness issues, diagnose and
treat patients as problems occur. Problem: A child has a middle ear
infection requiring an antibiotic that is dosed at 60 mg per kg a
day and divided into 3 doses per day. The medication is supplied as
a suspension, 250 mg / 5 ml. 1. How many teaspoons is each dose for
a child weighing 48 pounds? 2. How many ounces of medicine should
the pharmacist dispense for an 8 day course of treatment? Facts
needed: 2.2 lbs = 1 kg 1 oz = 6 teaspoons 1 teaspoon = 5 ml 76.
Numbers and Operations: Family Physician Idaho Physicians
Associates Job Description: Educate patients on wellness issues,
diagnose and treat patients as problems occur. Problem: A child has
a middle ear infection requiring an antibiotic that is dosed at 60
mg per kg a day and divided into 3 doses per day. The medication is
supplied as a suspension, 250 mg / 5 ml. 1. How many teaspoons is
each dose for a child weighing 48 pounds? 2. How many ounces of
medicine should the pharmacist dispense for an 8 day course of
treatment? Facts needed: 2.2 lbs = 1 kg 1 oz = 6 teaspoons 1
teaspoon = 5 ml Solution: 1. How many teaspoons per dose? 48 lb 2.2
lbs/kg = 21.8181 kg x 60 mg/kg = 1309.09 mg per day 1309.09 mg 3
doses = 436.36 mg per dose 250 mg of medication in 5 ml / 1 tsp = 5
ml = 250 mg of medication 436.36 mg 250 mg/tsp = 1.7454545 = 1.75
teaspoons per dose 2. How many ounces of medicine for 8 days of
treatment? 3 doses/day x 8 days x 1.75 tsp/dose = 42 tsp of
medicine 42 tsp 6 tsp/ounce = 7 ounces of medicine 77.
Algebra/Geometry: Utility Facility Representative Idaho Power Job
Description: Design and layout overhead and underground power
lines. Problem: Determine the downward force (V) exerted on the
pole by a down guy holding 3 conductors and determine the tension
on the guy wire. V (Vertical Force) = (#of conductors) x T Tan G
(Guy Wire Tension) = (# of conductors) x T Sin T = Tension of each
conductor = 4,073 lbs H = Height of attachment = 35 ft L = Length
of anchor lead = 21 ft Because this is a static system, the sum of
the horizontal forces = 0 and the sum of the vertical forces = 0.
78. Algebra/Geometry: Utility Facility Representative Idaho Power
Job Description: Design and layout overhead and underground power
lines. See problem for details. Solution: Step one: Determine : tan
= opposite = 21 = 0.6 adjacent 35 = Tan-1 (0.6) = 31 Step two:
Determine the guy wire tension G We can get G by summing the
horizontal forces. F (horizontal direction) = 0 because the system
is static. -G sin + 3 (4073 lbs) = 0 G = 3 x 4073 lbs = 12219 sin
sin 31 G = 23,750 lbs Step three: Determine the vertical force V:
We can get the compression force on the pole by summing the forces
in the vertical direction. F (vertical direction) = 0 because the
system is static. -G cos + V = 0 V= G cos = 23,750 lbs * cos 31 =
20,358 lbs 79. Geometry: GIS Analyst Idaho State Tax Commission Job
Description: Perform geographical analysis on land values, land
types, and determine fair market values over different geographical
areas. Problem: Jim, an appraiser, needs to find the value of a lot
in a subdivision. He knows that land prices in this particular area
are selling at $6.25 per square foot. Jim has the following lot to
appraise, but he must first find the square footage to determine
the appraised value of the lot. 80. Geometry: GIS Analyst Idaho
State Tax Commission Job Description: Perform geographical analysis
on land values, land types, and determine fair market values over
different geographical areas. Problem: Jim, an appraiser, needs to
find the value of a lot in a subdivision. He knows that land prices
in this particular area are selling at $6.25 per square foot. Jim
has the following lot to appraise, but he must first find the
square footage to determine the appraised value of the lot.
Solution: Area of circle = r2 Area of circle = (r2 )/2 = ((25)2 )/2
= 981.75 sq. ft. Area of square = length x width = 75 ft. x 50 ft.
= 3,750 sq. ft. Square + half circle = 3,750 + 981.75 = 4,731.75
sq. ft. $6.25 x 4,731.75 = $29,573.44 81. Numbers and Operations:
Tax Analyst Idaho State Tax Commission Job Description: Analyzes
and audits tax returns prepared by State of Idaho residents.
Problem: A person has $20,000 that is taxable at a tax rate of 7%.
She files the return 35 days after the due date. The interest rate
for late payment is 9% a year, assessed on a daily basis. The late
payment penalty is 5% per month for each month or partial month
after the due date, to a maximum of 25%, or $10.00 whichever is
greater. 1. What is the total tax? 2. What is the penalty? 3. What
is the interest due? 4. What is the total due? 82. Numbers and
Operations: Tax Analyst Idaho State Tax Commission Job Description:
Analyzes and audits tax returns prepared by State of Idaho
residents. Problem: A person has $20,000 that is taxable at a tax
rate of 7%. She files the return 35 days after the due date. The
interest rate for late payment is 9% a year, assessed on a daily
basis. The late payment penalty is 5% per month for each month or
partial month after the due date, to a maximum of 25%, or $10.00
whichever is greater. 1. What is the total tax? 2. What is the
penalty? 3. What is the interest due? 4. What is the total due?
Solution: 1. The total tax due is found by multiplying the taxable
amount ($20,000) times the tax rate (7%). $20,000 x .07 = $1,400
tax 2. The total penalty due is calculated by multiplying the
taxable amount ($20,000) times the tax rate (7%) times the interest
rate (9%) times the number of days late (35) divided by the number
of days in the year (365). ($20,000 x .07 x .09 x 35 days) 365
days/yr = $12.08 penalty 3. The total interest due is calculated by
multiplying the taxable amount ($20,000) times the tax rate (7%)
times the months late (2) times the payment penalty (5%). $20,000 x
.07 x 2 months x .05 = $140 interest 4. Therefore, the total tax,
penalty and interest due is calculated by adding these three
amounts together. $1,400.00 + $12.08 + $140.00 = $1,552.08 total
This type of calculation would be done by anyone filing tax returns
and by Tax Commission personnel in positions ranging from clerical
staff to auditors or compliance officers. The salary range of those
positions ranges from $14,000 to $35,000. 83. Algebra: Financial
Analyst Interstate Food Processing Corporation Job Description:
Provide analyses as required to ensure the organization is meeting
its financial objectives. Functions include preparation of budgets,
analysis of profitability by customer and product, and the
estimation of new products costs and prices. Problem: Businesses
generally incur two types of expenses: fixed and variable. Fixed
expenses are those that do not change with the amount of business.
For example, in our business we have certain costs such as rent,
electricity, and some employee wages (customer service
representatives and billing clerks) that do not change whether we
make one sale or one hundred sales. Variable costs, however,
increase directly with the amount of sales. In our business, these
costs would include items such as raw products, packaging materials
(bags and boxes), and the wages of employees that produce the
items. Each time we introduce a new product, we estimate how many
cases per month we must sell in order to pay for the fixed costs of
the operation and begin to make a profit. This estimate is called a
Break-Even Analysis and is the point where total sales revenue
equals total (fixed and variable) costs. The difference between the
Selling Price per case and the Variable Costs per case is called
the Contribution Margin. Determine the number of cases that must be
sold to reach the break even point. The following information is
available to solve the problem: Selling price per case (P) $8.95
Variable cost per case (V) $6.45 Fixed Costs per month (F)
$24,000.00 Quantity of cases (Q) ? Break even Quantity (QBE) QBE =
F / (P-V) 84. Algebra: Financial Analyst Interstate Food Processing
Corporation Job Description: Provide analyses as required to ensure
the organization is meeting its financial objectives. Functions
include preparation of budgets, analysis of profitability by
customer and product, and the estimation of new products costs and
prices. See problem for details. Solution: The breakeven point is
reached when costs equals profits. F + V Q = P Q $24,000.00 + 6.45
Q = 8.95 Q QBE = F / (P-V) QBE = $24,000.00 / ($8.95 - $6.45) =
9,600 cases 85. Measurements: Property Manager (1) J. D. Property
Job Description: Owns, operates and manages rental properties.
Oversees or does all maintenance and/or repairs on houses and
property. Problem: You need to pour a new sidewalk that is 4' wide,
16' long, and 4" thick. Concrete costs $70.00/cubic yard. 1) How
many cubic yards of concrete are required? 2) How much will the
concrete cost? 86. Measurements: Property Manager (1) J. D.
Property Job Description: Owns, operates and manages rental
properties. Oversees or does all maintenance and/or repairs on
houses and property. Problem: You need to pour a new sidewalk that
is 4' wide, 16' long, and 4" thick. Concrete costs $70.00/cubic
yard. 1) How many cubic yards of concrete are required? 2) How much
will the concrete cost? Solution: 1 yard = 3 feet 1 cubic yard = 3
ft x 3 ft x 3ft 1 cubic yard = 27 cubic feet (ft) 4 inch = 1/3 foot
4 ft x 16 ft x 1/3 ft = 21.3 ft 1) 21.3 ft x 1yd 27 ft = 0.79 cubic
yards needed 2) .79 cubic yards x $70.00 / cubic yard = $55.30 87.
Measurements: Property Manager (2) J. D. Property Job Description:
Owns, operates and manages rental properties. Oversees or does all
maintenance and/or repairs on houses and property. Problem: You
need to build a wall using 2x4s covered with 4' x 8' sheet rock.
The wall is 20 feet long and 8 feet high. 1) How many 2x4s are
required if the 2x4s are on 16" centers, spaced 16 apart? 2) How
many sheets of sheet rock will be needed? 88. Measurements:
Property Manager (2) J. D. Property Job Description: Owns, operates
and manages rental properties. Oversees or does all maintenance
and/or repairs on houses and property. Problem: You need to build a
wall using 2x4s covered with 4' x 8' sheet rock. The wall is 20
feet long and 8 feet high. 1) How many 2x4s are required if the
2x4s are on 16" centers, spaced 16 apart? 2) How many sheets of
sheet rock will be needed? Solution: 1) 20 feet x 12 inches/foot =
240 inches 240 inches 16 inch centers = 15 spaces + 1 = 16 (8-foot
2x4s) 2) 20 feet 4-foot sheets = 5 sheets of sheet rock 89.
Measurements: Property Manager (3) J. D. Property Job Description:
Owns, operates, and manages rental properties. Oversees or does all
maintenance and/or repairs on houses and property. Problem: You
need to re-roof a house with composite shingles. Each side of the
roof is 20 feet by 40 feet. How many packages of shingles are
required and how much will it cost? Each package of shingles covers
12 square feet (ft) and costs $7 plus another $12 to have it put on
the roof (for labor and other materials such as nails). 90.
Measurements: Property Manager (3) J. D. Property Job Description:
Owns, operates, and manages rental properties. Oversees or does all
maintenance and/or repairs on houses and property. Problem: You
need to re-roof a house with composite shingles. Each side of the
roof is 20 feet by 40 feet. How many packages of shingles are
required and how much will it cost? Each package of shingles covers
12 square feet (ft) and costs $7 plus another $12 to have it put on
the roof (for labor and other materials such as nails). Solution:
1. 20 ft x 40 ft = 800 ft x 2 = 1600 ft roof 1600 ft 12 ft
coverage/pkg = 133.3 or 134 packages of shingles 2. 134 packages x
$7 per package = $938 for shingles 134 packages x $12 = $1608 for
labor/materials $938 + $1608 = $2546 roof installed 91.
Measurements/Geometry: Architect James Gipson Associates Problem:
#1 John and Joan are planning a new home. They want as much window
area as possible. The local energy code permits a maximum window
area of 17% of the house floor area. The windows John and Joan will
use are each 3 ft. x 5 ft. and the floor area of the house is 1,720
square feet. How many windows can they put into their new house? #2
Karen is figuring how many bundles of shingles to order for the
roof on a garage. The garage is 24 ft. x 24 ft., with a single roof
ridge down the middle, plus a 2 ft. overhang all around. Three
bundles of shingles are required for each 100 sq. ft. of roof. How
many bundles of shingles should Karen order? 92.
Measurements/Geometry: Architect James Gipson Associates Problem:
#1 John and Joan are planning a new home. They want as much window
area as possible. The local energy code permits a maximum window
area of 17% of the house floor area. The windows John and Joan will
use are each 3 ft. x 5 ft. and the floor area of the house is 1,720
square feet. How many windows can they put into their new house? #2
Karen is figuring how many bundles of shingles to order for the
roof on a garage. The garage is 24 ft. x 24 ft., with a single roof
ridge down the middle, plus a 2 ft. overhang all around. Three
bundles of shingles are required for each 100 sq. ft. of roof. How
many bundles of shingles should Karen order? Solution: #1 17% of
1,720 sq. ft. = 292.4 sq. ft. Each window is 3' x 5' or 15 sq. ft.
292.4 15 = 19.49 Therefore, John and Joan can have at most 19
windows. #2 Consider the end view of the roof as two right
triangles, each with a base of 12' + 2' = 14' and a height of 7'. a
+ b = c 7 + 14 = c = 245 sq. ft. c= 15.65 ft. Area of half the roof
= 15.65' x (24'+ 4') = 438.2 sq. ft. Area of the roof = 438.2 x 2 =
876.4 sq. ft. The number of shingle bundles required = area of roof
33 1/3 876.4 33 1/3 = 26.29 Therefore, Karen should order 27
bundles. 93. Geometry: Excavator John Sawyer Excavation Job
Description: Digging foundations for businesses and houses Problem:
The following problem is used to make sure houses and buildings are
"square" (sides form right angles). If the length of one side of
your house is 44 feet and the adjacent side is 68 feet, show that
all corners form 90-degree angles. The diagonals of a rectangle
have equal measure. Show that the diagonals of the following
figures are equivalent. 94. Geometry: Excavator John Sawyer
Excavation Job Description: Digging foundations for businesses and
houses Problem: The following problem is used to make sure houses
and buildings are "square" (sides form right angles). If the length
of one side of your house is 44 feet and the adjacent side is 68
feet, show that all corners form 90-degree angles. The diagonals of
a rectangle have equal measure. Show that the diagonals of the
following figures are equivalent. Solution: Use the Pythagorean
Theorem. 44 + 68 = x 6560 = x 80.99 = x 81 ft. = x If this number
is equal to the length of your diagonals when measured, you will
have 90-degree angles. 95. Algebra: Finance J.R. Simplot Company
Job Description: Indebtedness compliance reporting, prospective
lender correspondence, asset leasing, and various other financial
analysis projects. Problem: Financial Indebtedness Covenant (this
is an example problem. Amounts are not actual, as the company does
not release financial information). A Company needs cash to expand
its current production facilities and has decided to borrow from
the bank. As one of the conditions of borrowing from the bank, the
Company agrees that its leverage ratio (total borrowings to total
shareholders' equity) will not exceed 1.25 to 1.0. The Company has
no current borrowings. Shareholders' equity is composed of
shareholders' contributions of cash and accumulated company
earnings. 1. If current shareholders' equity is 300, what is the
maximum amount the Company can currently borrow? 2. If the Company
wishes to reserve 50% of its maximum available borrowing for future
needs, how much will it borrow currently? 3. If the Company needs
to borrow 425 for the expansion and earns 10 per month, how many
months must it accumulate earnings before qualifying for the loan
of 425? (Remember current shareholders' equity). 96. Algebra:
Finance J.R. Simplot Company Job Description: Indebtedness
compliance reporting, prospective lender correspondence, asset
leasing, and various other financial analysis projects. Problem:
Financial Indebtedness Covenant (this is an example problem.
Amounts are not actual, as the company does not release financial
information). A Company needs cash to expand its current production
facilities and has decided to borrow from the bank. As one of the
conditions of borrowing from the bank, the Company agrees that its
leverage ratio (total borrowings to total shareholders' equity)
will not exceed 1.25 to 1.0. The Company has no current borrowings.
Shareholders' equity is composed of shareholders' contributions of
cash and accumulated company earnings. 1. If current shareholders'
equity is 300, what is the maximum amount the Company can currently
borrow? 2. If the Company wishes to reserve 50% of its maximum
available borrowing for future needs, how much will it borrow
currently? 3. If the Company needs to borrow 425 for the expansion
and earns 10 per month, how many months must it accumulate earnings
before qualifying for the loan of 425? (Remember current
shareholders' equity). Solution: 1. Maximum borrowing = 1.25 x
Shareholders' equity (Financial Covenant) 375 = 1.25 x 300 2.
Current borrowing = 50% x Maximum borrowing 187.5 = 50% x 375 3.
Borrowing needs = 1.25 x [Current Shareholders' Equity + (Monthly
Earnings x Number Months)] 425 = 1.25 x [300 + (10 x number of
months)] 425 = 375 + 12.5 x (number of months) (425-375) 12.5 =
number of months 4 = number of months 97. Numbers and Operations:
Financial Services Vice President Key Bank Job Description:
Providing commercial loans, leases, derivative products and cash
management. Problem: Determine the gain on the investment. Stock is
purchased @ $21 1 4 per share Stock is sold @ $34 1 8 per share
Shares owned: 1,280 98. Numbers and Operations: Financial Services
Vice President Key Bank Job Description: Providing commercial
loans, leases, derivative products and cash management. Problem:
Determine the gain on the investment. Stock is purchased @ $21 1 4
per share Stock is sold @ $34 1 8 per share Shares owned: 1,280
Solution: 34 1 8 - 21 1 4 = 34.125 - 21.25 = 12.875 (the difference
between selling price and buying price/share) $12.875 x 1280 shares
of stock = $16,480 gain 99. Geometry/Numbers &
Operations/Measurements: Glass Installer Klassic Glass & More
Job Description: Cut and install glass - both auto and residential.
Problem: You need to cut a mirror, but all of the measurements are
in inches instead of feet. Find the length of each side in feet to
cut a piece of glass and find the total square feet in the mirror.
100. Geometry/Numbers & Operations/Measurements: Glass
Installer Klassic Glass & More Job Description: Cut and install
glass - both auto and residential. Problem: You need to cut a
mirror, but all of the measurements are in inches instead of feet.
Find the length of each side in feet to cut a piece of glass and
find the total square feet in the mirror. Solution: 48 inches 12
in/ft = 4 feet (width) 84 inches 12 in/ft = 7 feet (length) 4 ft x
7 ft = 28 square feet in mirror 101. Numbers and Operations:
Director of International Finance Lamb Weston Job Description:
Directs accounting functions in Holland, Turkey and India for the
sale, manufacturing, and distribution of Frozen French Fries.
Problem: Company A is a manufacturer and seller of French Fries and
owns 40% of a similar company in Germany (Company G). Company G
sells French Fries throughout Europe. Company G sells 30,000,000
pounds of French Fries per year in Belgium alone. The customers in
Belgium pay Company G in Belgian Franks. Company G keeps their
financial records in German Marks; however, Company G reports
profits to Company A in U.S. Dollars. How much money will Company A
make in one year from sales of Company G's fries to Belgium, given
the financial information below? Currency Conversion Table 1 U.S.
Dollar = 1.50 German Marks 1 German Mark = 20 Belgian Franks 1 U.S.
Dollar = 30 Belgian Franks 1. Average sales price per pound in
Belgium: 10 Belgian Franks/pound. 2. Average cost to
produce-per-pound in Germany: 0.40 German Marks (cents)/pound. 102.
Numbers and Operations: Director of International Finance Lamb
Weston Job Description: Directs accounting functions in Holland,
Turkey and India for the sale, manufacturing, and distribution of
Frozen French Fries. See problem page for details. Solution:
Revenue: 30,000,000 pounds x 10 Belgian Franks = 300,000,000
Convert to dollars: 300,000,000 30 Franks/dollar = $10,000,000
Cost: 30,000,000 pounds x 0.40 German Marks = 12,000,000 Convert to
dollars: 12,000,000 1.50 Marks/dollar = $8,000,000 Revenue - Cost =
Profit $10,000,000 - $8,000,000 = $2,000,000 (Company G) 40% of
profit belongs to Company A. Therefore, $2,000,000 x 0.40 =
$800,000 is the profit of Company A from sales in Belgium. 103.
Geometry: Contractor Lamm Construction Job Description: Residential
construction Problem: A builder needs to place a house on a lot
that has no parallel sides. How would he place the house on the lot
and make sure the house is square on the lot? 104. Geometry:
Contractor Lamm Construction Job Description: Residential
construction Problem: A builder needs to place a house on a lot
that has no parallel sides. How would he place the house on the lot
and make sure the house is square on the lot? Solution: Find the
starting point marked (D). Measure the width of the house to find
the distance (DE). Measure the length to find distance (EF). If DF
= (FE) + (DE) , then the house is square on the lot as proved by
the Pythagorean theorem. 105. Algebra/Geometry: Manufacturer Lawn
Mower Factory Job description: Manufacture lawn mower parts &
lawn mowers Problem: A worker in a lawnmower factory is asked to
make the part shown below for a new lawnmower design. To program a
machine to cut the part out, the worker must find the slope and
length of edge D. 106. Algebra/Geometry: Manufacturer Lawn Mower
Factory Job description: Manufacture lawn mower parts & lawn
mowers Problem: A worker in a lawnmower factory is asked to make
the part shown below for a new lawnmower design. To program a
machine to cut the part out, the worker must find the slope and
length of edge D. SOLUTION: 107. Numbers and Operations: Property
Development Manager L.B. Industries, Inc. Job Description: Locate
potential sites, negotiate purchases, coordinate analysis of
attorneys and engineers, coordinate pre-purchase due diligence,
determine lot configuration and pricing, oversee development of
sites, and negotiate sales. Problem: The Eagle Land Company has the
opportunity to purchase 76.80 acres of land in Boise, near the
Cole/I-84 Interchange, for $20,000 an acre. The property is zoned
for light industrial and retail use. Developed property of this
sort is currently selling for $3.50 a square foot. As configured,
it appears that 415,000 square feet of the land will need to be
dedicated as non-sellable roadways, sidewalks and median strips.
Engineering fees and improvements (including sewer lines,
telephone, electrical power, curbs and gutters) will cost the
company an additional $1,250,000.00. To receive an adequate profit
after salaries, interest charges, realtors' fees and other fixed
costs, the Eagle Land Company must receive a mark up of at least
150% above the dollar amount of its purchase and development costs
(250% of the total cost of the development.) Commercial lots are
generally sold on a square footage basis. 1. What is the minimum
price Eagle Land Company must receive, on a square footage basis,
for the land in this subdivision? (Hint: An acre contains 43,560
square feet.) 2. Does it make economic sense for Eagle Land Company
to purchase this property? Support your conclusion. 108. Numbers
and Operations: Property Development Manager L.B. Industries, Inc.
Job Description: Locate potential sites, negotiate purchases,
coordinate analysis of attorneys and engineers, coordinate
pre-purchase due diligence, determine lot configuration and
pricing, oversee development of sites, and negotiate sales. See
problem page for details. Solution: 1. What is the minimum price
Eagle Land Company must receive, on a square footage basis, for the
land in this subdivision? Cost of land:76.80 acres x $20,000/acre =
$1,536,000 Total cost to develop the subdivision equals cost of
land plus cost of engineering and improvements: $1,536,000 +
$1,250,000 = $2,786,000 The total minimum price equals total cost
to develop the subdivision times 250%: $2,786,000 x 2.50 =
$6,965,000 Total square footage in the development equals total
acres times square footage per acre: 76.80 acres x 43,560 sq
ft/acre = 3,345,408 square feet Total sellable square footage
equals total square footage in the development less square footage
to be dedicated as roadways, sidewalks and median strips: 3,345,408
sq ft - 415,000 sq ft = 2,930,408 sq ft The minimum sales price per
square foot equals the total minimum sales price for the
subdivision divided by the sellable square footage in the
development: $6,965,000.00 2,930,408 sq ft = $2.3768021 or $2.38/sq
ft 2. Does it make economic sense for Eagle Land Company to
purchase this property? Yes, this land can be sold for $3.50 per
square foot and $2.38 per square foot will insure an adequate
profit. If the land is sold for $3.50 per square foot, the Eagle
Land Company would receive an additional profit of $1.12 per square
foot above the amount it deems to be an adequate profit. At
2,930,408 square feet of sellable land in the entire development,
the additional $1.12 per square foot would result in an extra
$3,282,056.90 in profit on property that cost $2,786,000 to
develop. 109. Measurements/Geometry: Homemaker Seamstress Lori
Purcell Job Description: All around handywoman: painter, carpenter,
seamstress, cook, and yard and home maintenance. Problem: A
homemaker wants to save money by making bedroom curtains rather
than buying them. Using the following information, determine how
much fabric she will need and how much the fabric will cost. Window
dimensions: 6' wide, 4' long. The finished width of the curtains
will be 3 times the window width. The curtains will have two
gathered sections with a 3" hem at the bottom and a 1" hem on each
side. The uncut fabric is 54" wide and costs $15.99 per yard.
Fabric is sold by the yard with partials in 1/2, 1/4, or 1/3 yard.
You will need to add 1/2 inch for seam allowances on sides, top and
bottom. A seam is where the fabric is sewn together; the allowance
is the material that is folded back on either side of the seam. Add
6" for curtain-rod pocket at the top. 110. Measurements/Geometry:
Homemaker Seamstress Lori Purcell Job Description: All around
handywoman: painter, carpenter, seamstress, cook, and yard and home
maintenance. See problem for details. Solution: 1. Find the
dimensions of the window in inches. Window width: 6 x 12 = 72"
Window length: 4 x 12 = 48" 2. Curtain width: the curtains will be
3 times the width of the window. 72" wide x 3 = 216" total width of
the curtains 216" 2 sections = 108" width of each section 3. Add
the side hems and seam allowances to the width of one section. 108"
+ 2" (2 side hems) + 1" (2 seam allowances) = 111" 111" represents
the cut fabric width 4. Because the fabric width is 54" long, 3
fabric widths will be required for one section (111 inches). This
will add another seam or 2 additional seam allowances. The cut
fabric width will now be 111" + 1" = 112" 5. To make the curtains,
5 fabric widths will be required. (2 widths plus a few inches for
each section.) Rather than buying 3 widths for each curtain, buy 2
for each curtain and share the extra width. 6. Curtain length =
window length + hem + seam allowance + rod pocket 48" + 3" + 1" +
6" = 58" (fabric length per curtain) 7. For the curtains, 5 lengths
of fabric will be needed. Each length will be 58" long. 58" x 5 =
290" 36"/yd = 8 yards + 2 inches She must purchase 8.25 yards,
since .25 is the smallest division 8. Cost of fabric: 8.25 yards x
$15.99 (cost per yard) = $131.92 111. Numbers and Operations:
Salesperson Shoe Department Macy's Job Description: Helps the
customer purchase a pair of shoes. Problem: The wage rate for a
salesperson at Macy's is $8.60 per hour for a 40 hour week and 1.5
times the base pay ("time and a half") for overtime. If a
salesperson works 48 hours in one week, how much is the gross
salary she or he earns? 112. Numbers and Operations: Salesperson
Shoe Department Macy's Job Description: Helps the customer purchase
a pair of shoes. Problem: The wage rate for a salesperson at Macy's
is $8.60 per hour for a 40 hour week and 1.5 times the base pay
("time and a half") for overtime. If a salesperson works 48 hours
in one week, how much is the gross salary she or he earns?
Solution: 1. Find the salary for the first 40 hours. $8.60 x 40 =
$344.00 2. Find the salary for the 8 hours overtime. 1.5 x $8.60 =
$12.90/hour x 8 hours = $103.20 3. Add the two amounts together.
$344.00 + $103.20 = $447.20 113. Algebra: Medical Technologist
Mercy Medical Center Job Description: Performs testing on blood and
body fluids to aid in diagnosis and treatment of disease. Problem:
Creatinine is a waste product of muscle metabolism normally found
at relatively constant levels in the blood. By measuring the plasma
and urine levels of creatinine, in a specific period of time, the
creatinine clearance or glomerular filtration rate can be
calculated. The creatinine clearance is used to determine the
extent of nephron damage in known cases of renal disease, to
monitor effectiveness of treatment and to determine the feasibility
of administering medications which can build up to toxic levels if
the glomerular filtration rate is markedly reduced. Using a urine
creatinine of 96 mg/dL (U), plasma creatinine of 1.3 mg/dL (P), and
urine volume of 125 mL from a 2 hour specimen (V), calculate the
glomerular filtration rate (creatinine clearance [C]