Activator You bought a shirt that was 45% of the original price. The shirt was $27. What was the original price?

Activator

• You bought a shirt that was 45% of the original price. The shirt was $27. What was the original price?

http://www.brainpop.com/math/ratioproportionandpercent/percents/

Percents of a Number

• This phrase will help you set up and solve all problems involving percent.

• Is over of = percent over 100= is/of = %/100

• The question will tell you where each number should go using is, of, and percent

Is / of = % / 100

What is 20% of 60 12 is 20% of what number

12 is what % of 60Or

What % is 12 of 60

= ==

Is / of = % / 100

What is 20% of 60 12 is 20% of what number

is 20

60 100

You may use any method to solve this proportion that you prefer.

= 12 %

60 100


= 12 20

of 100


=

12 is what % of 60Or

What % is 12 of 60

Set up each problem using the proportionSolve.

Set up the proportion of each problemNumber the problem, do not erase, I will

check all three.

Another way to solve % of number problems:

Another way to solve % of number problems:

Here is an easy way to remember how to write the equation:

Is = % of number

If you substitute the word of for the times sign it will help you set your equation up correctly.

Homework

• Workbook pg. 87-88

Activator

• Chris bought a sweater that had been marked up 23% by the retail store, but he had a coupon for 15% off. The sweater was originally $56 before the mark up. How much was the mark up? How much was the discount his coupon gave him? What was the total if he paid 9% sale tax?

Finding Discounts

• Discounts are the money you save on a purchase.

• 2 things to be aware of: 1. If the question asks for the discount you are just

finding the money you saved.

2. If the question asks for the “sale price” or “discounted price” you are finding the new total. (subtract the discount from the original price)

Finding Discounts

• To find discount:

Percent saved x Original Price = Discount

• To find “sale price” or “discounted price”

Original Price – Discount = Sale Price$ - ($ x %)

Assessment Prompt

• What must you do to the % before you solve the problem?

Finding Discounts

• Mark bought a sweater that was on sale for 30% off the original price of $48.00. How much did he save? What was the sale price?

1. How much did he save: % x op =

2. What was the sale price: op – (% x op) =

Assessment Prompt

• What is the difference between a discount and the sale price?

• How do you find the sale price?

Finding Mark Ups

• Mark ups are how much money was added to the price from the manufacturer to the retailer.

• 3 things to be aware of: 1. If the question asks for the mark up you are just

finding the money that the item increased. 2. If the question asks for the “price” or “retail price”

you are finding the new total. (add the mark up to the original price)

3. Sometimes the original price is called the “wholesale price”

Finding Mark Ups

• To find mark ups:

Percent marked up x wholesale Price = mark up

• To find “price” or “retail price”

Original Price + Mark up = Retail Price

$ + ($ x %)

Finding Mark Ups

• Mark bought a bottle of shampoo that was wholesale for $2, but Wal-mart marked up the price 200% How much was the mark up? What is the retail price?

1. How much was the mark up: % x ws p =

2. What is the retail price: ws p + (% x ws p) =

Assessment Prompt

• How are finding mark ups and discounts similar?

Find the Sale Price: You find a sweater on sale for 30% off. The sweater is originally $72. What is the sale price of the sweater?

Assessment Prompt

• What is the difference between a markup and a discount?

• How do you find the retail price?

Homework

• Worksheet 7.6 #1-7 and #18-21

Finding Sales Tax

• Sales tax is the money you pay extra for taxes.

• 3 things to be aware of: 1. If the question asks for the sales tax you are just

finding the money you pay extra.

2. If the question asks for the “total cost” or “cost” you are finding the new total. (add the sales tax to the original price)

3. Tax is always found after you take off the discount or add the markup.

Finding Sales Tax

• To find sale tax:

Percent taxed x Original Price = sales tax % x $ = sales tax

• To find “total cost” or “cost”

Original Price + sales tax = total cost

$ + sales tax = total cost or $ + (% x $) = total cost

Finding Sales Tax

• Mark bought a sweater that was $48.00. The tax for his state is 8.75%. How much was the tax? What was the total cost?

1. How much was the tax: % x op =

2. What was the total cost: op + tax=

Finding Tips

• Tips are the money you give someone for a good job.

• 2 things to be aware of: 1. If the question asks for the tip you are just

finding the money you leave.

2. If the question asks for the “total cost” or “cost” you are finding the new total. (add the tip to the original price)

Finding Tips

• To find tip:

Percent tip x Original Price = tip% x $ = tip

• To find “total cost” or “cost”

Original Price + tip Total Cost

$ + tip = total cost or $ + (% x $) = total cost

Finding Tip

• Mark and his family went to dinner at Olive Garden. Their food bill was $56.78. They want to leave a 15% tip for their server. The tax is 9.5% How much was your tip? How much was your tax? What was the total cost of the meal?

Short Cut for finding the total cost and retail price

add 100% to your % then multiply that % by the original price.

Example: Cost = $5.62 tax rate = 6%

Tax = $5.62 x 6% = 0.3372 rounds to 0.34.

Total= 5.62 + 0.34= 5.96

$5.62 x 106% = $5.9572 = $5.96

TOD1. What is the first step to solving for discounts,

markups, sales tax, and tips?

2. Which of these four increases the price?

3. Which of the these four decreases the price?

4. Of discounts, markups, and sales tax, which do you always do last in the problem?

5. Cost: $58 Tax: 7% Discount: 15%: Find the total cost.

Summarizer

• Chris bought a sweater that had been marked up 23% by the retail store, but he had a coupon for 15% off. The sweater was originally $56 before the mark up. How much was the mark up? How much was the discount his coupon gave him? What was the total if he paid 9% sale tax?

Workbook pg. 95-96

Simple Interest

• How many of you have your own bank account?

• Do you know what happens every 3, 6, or 12 months?

• How many have heard the term refinancing? What does it mean?

Copy the box:

Simple Interest• To Find Simple Interest use the following

formula: I = Prt

• I = interested earned • P= Principal ($ you started with) • R = Annual interest rate or (%) • T = Time in years. (if the time is given in months,

write the month as a fraction over 12: Example 7 months = 7/12)

Copy all above

Real Life• You buy a house for $105,000. You are

paying an interest rate of 6.12% for a period of 30 years. How much interest will you pay? How much will you pay total for this house?

I = Prt

I = 105,000(6.12%)(30)

I = $192,780

B = $297,780

-

Simple Interest• To find a balance: you add the interest to the principal. • P + I = balance (if you don’t know the interest or principal you will need to

solve for them)

• If the balance is given then you will need to subtract either the interest or the principal from the balance to find the (interest or principal)

• To find any missing part of the Interest formula: You multiply to two pieces of information given and then divide the

interest by that product.

Example: You want to find the rate: $450 = $300 x (r) x 3 years$450 = 900r 900 900

0.5 = r = 50% try to turn you decimals for rates back into percent form.

Using I = prt

• You deposit $600 into a 6 month CD. After 6 months, the balance is $618. What is the interest rate?

• *The interest earned is the balance minus the principal! **1/2 year =0.5. ($18 is the interest because you started with $600 and had a balance of $618 so you would subtract them)

I = prt18 = 600 * r * 0.518 = 300r (divide both sides by 300)300 300

0.06 = r, so the rate is 6%.

Pair/Share• You deposit $1000 into a 3-month

certificate of deposit (CD). After 3 months the balance is $1005. Find the simple annual interest rate!

I = Prt

$5 = $1000 x r x 3/12

$5 = 250r

250 250

0.02 = r = 2%

Again!• Find the time: You put $750 into a CD. Your

simple annual interest rate is 4%. How long will it take you to earn $150 in interest?

• I = Prt

• Find the principal: You earn $84 interest on a 2-year CD that pays 7%. What was the original principal?

• I = Prt

Homework 99-100

Solve: You have a principal of $540 with a rate of 3.5% for 8 years. What will your balance be?

How do you find the interest if you

know the balance and the principal?

Find the missing valueI= 40P= $520 R=T= 3 years

Solve: You have a principal of $2200 with a rate of 6% for 8 months. What will your balance be?

How do you find the principal if you

know the interest and the

balance?

Find the missing valueI=P= $780 R= 7.5%T= 4 months

Solve: You have a principal of $758 with a rate of 0.25% for 5 years. What will your balance be?

How do you find simple interest?

Find the missing valueI= 120P= $1260 R= 5%T=

Tic-Tac-Think: Simple Interest Choose one task from each column to answer completely.

Activator• Sam bought an Under Amour Hoodie for $65.

After a year he out grew it. He sold the hoodie at a garage sell for $5.

• Describe the change in price.

• What is the difference in price?

• How to find the percent a # is of another #.

Percent Increase or Decrease

Percent of change = Difference of the two numbers

Original amount


• Wal-mart sold a stereo for $98. Someone who bought that stereo was able to sell it on EBay for $118. What was the percent change?


• Set up the following problem:

Chris had 3 rabbits in May, by July he had 8.

In the following problem, what was the original figure?

451 – 247 / 247

Error Analysis• Chad bought a new basketball goal for his son for

$400. He saw the same goal three weeks later on sale for $250. What was the percent increase or decrease?

400-250 250

150 250 60% decrease

A school had 1214 students 5 years ago. Today the school has 1024 students. Find % of change.

What is the first step to identifying the

percent of change?

1589-254/254

Identify % of change.

You bought a baseball card for $0.25 and 20 years later sold it for $4.75. Find % of change.

What is the divisor in the percent of change formula?

2.587-1.04/2.587


Your grade the first 9 weeks was 87.5. the second 9 weeks was 93.2. Find the % change.

How do you identify if the change is an increase or decrease?

17-12/12


Tic-Tac-Think: % increase or decrease Choose one task from each column to answer completely.

Homework 93-94


What is the first step to identifying the percent of

change?

1589-254/254




2.587-1.04/2.587



How do you identify if the change is an increase or

decrease?

17-12/12



What is the first step to identifying the percent of

change?

1589-254/254




2.587-1.04/2.587



How do you identify if the change is an increase or

decrease?

17-12/12


Tip, Interest, Percent of a #Find a Tip

What percent is a number of another number

Simple interest Multiply the percent you want to

leave by the cost of the meal.

Or you could double the tax: This is about a twenty percent tip.

Or you can find 10% then half of that and add the two answers to get the total tip. Round to nearest whole number.

The Formula: Prt.

P= Principle x r=rate x t=time

You put $30 dollars in a savings account that earns 8% interest for 3 years how much will you earn.

30 x .08 x 3 = $7.20

What percent is 12 of 38? Write the problem as a fraction equal to another fraction with 100 on the bottom.

Example: 12 / 38 = ? / 100

Cross multiply the numerator and denominator diagonal of each other. Divide by the denominator not used.

12 x 100 = 1200 ÷ 38 = 31.58(rounded) or write the ratio as fraction, turn into a decimal, turn decimal into a percent: 12/38 = 12 ÷ 38 = 0.3157, move decimal right twice = 31.57%

All Percents Must be in decimal form before you multiply!!

Activator You bought a shirt that was 45% of the original price. The shirt was $27. What was the original price?

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