Name Ganiera, Dale Vincent CabigasSubject CE Elective 3
ChapterSection CE 5-2Date Submitted January 5, 2015
OBRERO CAMPUSDavao City ALGEBRA
[Type a quote from the document or the summary of an interesting
point. You can position the text box anywhere in the document. Use
the Drawing Tools tab to change the formatting of the pull quote
text box.]
Title:
______________________________________________________
(ABSTRACT)A.1.1. When the first of two numbers is added to twice
the second the result is 21, but the second number is added to
twice the first result is 18. Find the two numbers.
A.1.2. If the numerator and denominator of a certain fraction
are both increased by 3, the resulting fraction equals 2/3. If,
however, the numerator and denominator are both decreased by 2, the
resulting fraction equals . Determine the fraction.
A.1.3. Twice the sum of two numbers exceeds three times their
difference by 8, while half the sum is one more than the
difference. What are the numbers?
A.1.4. If three times the larger of two numbers is divided by
the smaller, the quotient is 6 and the remainder is 6. If five
times the smaller is divided by the larger, the quotient is 2 and
the remainder is 3. Find the numbers.
(AGE PROBLEMS)A.1.5 Six years ago Bob was four times as old as
Mary. In four years he will be twice as old as Mary. How old are
they now?
A.1.6. A is eleven times as old as B. In a certain number of
years A will be five times as old as B, and five years after that
he will be three times as old as B. How old are they now?
(DIGIT PROBLEMS)A.1.7. Three times the tens digit of a certain
two digit number is two more than four times the units digit. The
difference between the given number and the number obtained by
reversing the digits is two less than twice the sum of the digits.
Find the number.
A.1.8. When a certain two digit number is divided by the number
obtained by reversing the digits, the quotient is 2 and the
remainder is 7. If the number is divided by the sum of its digits,
the quotient is 7 and the remainder 6. Find the number.
(BUSINESS PROBLEMS)A.1.9. Two pounds of coffee and 3 lb. of
butter cost $4.20. A month later the price of coffee advanced 10%
and that of butter 20%, making the total cost of a similar order
$4.86. Determine the original cost of a pound of each.
A.1.10. If 3 gallons of Grade A oil are mixed with 7 gal of
Grade B oil the resulting mixture is worth 43 /gal. However, if 3
gal of Grade A oil are mixed with 2 gal of Grade B oil the
resulting mixture is worth 46 /gal. Find the price per gallon of
each grade.
A.1.11. An investor has $116 annual income from bonds bearing 3%
and 5% interest. Then he buys 25% more of the 3% bonds and 40% more
of the 5% bonds, thereby increasing his annual income by $41. Find
his initial investment in each type of bond.
(MIXTURE PROBLEMS)A.1.12. Tank A contains 32 gallons of solution
which is 25% alcohol by volume. Tank B has 50 gal of solution which
is 40% alcohol by volume. What volume should be taken from each
tank and combined in order to make up 40 gal of solution containing
30% alcohol by volume?
A.1.13. Tank A holds 40 gal of a salt solution containing 80 lb.
of dissolved salt. Tank B has 120 gal of solution containing 60 lb.
of dissolved salt. What volume should be taken from each tank and
combined in order to make up 30 gal of solution having a salt
concentration of 1.5 lb./gal?
A.1.14. A given alloy contains 10% zinc and 20% copper. How many
pounds of zinc and of copper must be melted with 1000 lb. of the
given alloy to produce another alloy analyzing 20% zinc and 24%
copper? All percents are by weight.
A.1.15. An alloy weighing 600 lb. is composed of 100 lb. copper
and 50 lb. tin. Another alloy weighing 1000 lb. is composed of 300
lb. copper and 150 lb. tin. What weights of copper and tin must be
melted with the two given alloys to produce a third alloy anlayzing
32% copper and 28% tin. All percents are by weight.
(MOTION PROBLEMS)A.1.16. Determine the speed of a motor boat in
still water and the speed of the river current, if it takes 3 hr.
to travel a distance of 45 mi upstream and 2 hr. to travel 50 mi
downstream.
A.1.17. When two cars race around a circular mile track starting
from the same place and at the same instant, they pass each every
18 seconds when travelling in opposite directions and every 90
seconds when travelling in the same direction. Find their speeds in
mi/hr.?
A.1.18. A passenger on the front of train A observes that he
passes the complete length of train B in 33 seconds when travelling
in the same direction as B and in 3 seconds when travelling in the
opposite direction. If B is 330 ft. long, find the speeds of the
two trains.
A.1.19. The first of three numbers exceeds the second by one
less than the third. The sum of the second and third numbers is one
more than the first. If the second is subtracted from the sum of
the first and third numbers the result is 5. Determine the
numbers.
A.1.20. When a certain three digit number is divided by the
number with digits reversed, the quotient is 2 and the remainder
25. The tens digit is one less than twice the sum of the hundreds
digit and units digit, If the units digit is subtracted from the
tens digit, the result is twice the hundreds digit. Find the
number.
A.1.21. The square of a certain number exceeds twice the square
of another number by 16. Find the numbers if the sum of their
squares is 208.
A.1.22. The diagonal of a rectangle is 85 ft. If the short side
is increased by 11 ft. and the long side decreased by 7 ft., the
length of the diagonal remains the same. Find the dimensions of the
original rectangle.
(RATIO, PROPORTION, AND VARIATION)A.1.23. If 8 men take 12 days
to assemble 16 machines, how many days will it take 15 men to
assemble 50 machines?
A.1.24. The distance covered by an object falling freely from
the rest varies directly as the square of the time of falling. If
an object falls 144 ft. in 3 sec., how far will it fall in 10
sec.?
A.1.25. The force of wind on a sail varies jointly as the area
of the sail and the square of the wind velocity. On a square foot
of sail the force is 1 lb. when the wind velocity is 15 mi/hr. Find
the force of a 45 mi/hr. wind on a sail of area 20 square
yards.
A.1.26. If 2 men can plow 6 acres of land in 4 hours, how many
men are needed to plow 18 acres in 8 hours?
(ARITHMETIC PROGRESSIONS)A.1.27. Three numbers are in the ratio
of 2:5:7. If 7 is subtracted from the second, the resulting numbers
form an A.P. Determine the original numbers.
A.1.28. Compute the sum of all integers between 100 and 800 that
is divisible by 3.
A.1.29. A freely falling body, starting from rest, falls 16 ft.
during the first second, 48 ft. during the second, second, 80 ft.
during the third second, etc. Calculate the distance it falls
during the fifteenth second and the total distance it falls in 15
seconds from rest.
A.1.30. In a potato race, 8 potatoes are placed 6 ft. apart on a
straight line, the first being 6 ft. from the basket. A contestants
starts from the basket and puts one potato at a time into the
basket. Find the total distance he must run in order to finish the
race.
(GEOMETRIC PROGRESSIONS)A.1.31. The first term of a G.P. is 375
and the fourth term is 192. Find the common ratio and the sum of
the first four terms.
A.1.32. In a geometric progression consisting of four terms in
which the ratio is positive, the sum of the first two terms is 8
and the sum of the last two terms is 72. Find the progression.
A.1.33. From a tank filled with 240 gallons of alcohol, 60
gallons are drawn off and the tank is filled up with water. Then 60
gallons of the mixture are removed and replaced with water, etc.
How many gallons of alcohol remain in the tank after 5 drawings of
60 gallons each are made?
A.1.34. A sum of $400 is invested today at 6% per year. To what
amount will it accumulate in five years if interest is compounded
a) annually, b) semi-annually, c) quarterly?
A.1.35. A man borrows $400 for 2 years at a simple interest rate
of 3%. Find the amount required to repay the loan at the end of 2
years.
A.1.36. What principal invested at 4% for 5 years will amount to
$1200?
A.1.37. A man wishes to borrow $200. He goes to the bank where
he is told that the interest rate is 5% interest payable in
advance, and that the $200 id to be paid back at the end of one
year. What interest rate is he actually paying?
A.1.38. A man wants to receive $800 immediately and pay it back
in 1 year. The bank charges a simple discount of 6% payable at
once. How much must he borrow?
A.1.39. What will $500 deposited in a bank amount to in 2 years
if interest is compound semi-annually at 2%?
A.1.40. A man expects to receive $2000 in 10 years. How much is
that money worth now considering interest at 6% compounded
quarterly? What is the discount?
A.1.41. Determine the present value of an annuity of $100 per
year at the end of each year for 5 years at 3% compound
annually.
A.1.42. What equal amount must a person invest at the end of
each year in order to have $20, 000 in 20 years if interest is 3%
compounded annually?
A.1.43. A mortgage debt in the amount of $8000 is to be
discharged (amortized) in 6 years by equal payments made at the end
of each year, the interest rate being 5% compounded annually. What
annual payments must be made? What is the total interest paid?
A.1.44. Determine the amount and present value of an annuity in
which n payments of R dollars are made at the beginning of each
payment period at an interest rate of i per payment period.
A.1.45. A student has a choice of 5 foreign languages and 4
sciences. In how many ways can he choose 1 language and 1
science?
A.1.46. In how many ways can 5 letters be mailed if there are 3
mailboxes available?
A.1.47. In how many different orders may 5 persons be seated in
a row?
A.1.48. Twelve different pictures are available, of which 4 are
to be hung in a row. In how many ways can this be done?
A.1.49. In how many orders can 7 different pictures be hung in a
row so that 1 specified picture is a) at the center, b) at either
end?
A.1.50. In how many ways can n men be seated in a row so that 2
particular men will not be next to each other?
A.1.51. Determine the number of different words of 5 letters
each that can be formed with the letters of the word chromate a) if
each letter is not used not more than once, b) if each letter may
be repeated in any arrangement. (These words need not have
meaning.)
A.1.52. How many 4-digit numbers may be formed with the 10
digits 0, 1, 2, 3, . . . , 9 if each digit is used only once in
each number? How many of these numbers are odd?
A.1.53. How many numbers between 3000 and 5000 can be formed by
using the 7 digits 0, 1, 2, 3, 4, 5, 6 if each digit must not be
repeated in any number?
A.1.54. How many signals can be made with 5 different flags by
raising them any number at a time?
A.1.55. a) How many arrangements can be made from the letters of
the word cooperator when all are taken at a time? How many of such
arrangements, b) have the three os together, c) begin with the two
rs?
A.1.56. a) In how many ways can 5 persons be seated at a round
table? b) In how many ways can 8 persons be seated at a round table
if 2 particular persons must always sit together?
A.1.57. By stringing together 9 differently colored beads, how
many different bracelets can be made?
A.1.58. In how many ways can 5 styles be selected out of 8
styles?
A.1.59. Determine the number of different triangles which can be
formed by joining the six vertices of a hexagon, the vertices of
each triangle being on the hexagon.
A.1.60.How many diagonal has an octagon?
A.1.61. There are 10 points in a plane. No three of these are in
a straight line, except 4 points which are all in the same straight
line. How many straight lines can be formed by joining the 10
points?
A.1.62. An organization has 25 members, 4 of whom are doctors.
In how many ways can a committee of 3 members be selected so as to
include at least 1 doctor?
A.1.63. Given 8 consonants and 4 vowels, how many 5-letter words
can be performed, each word consisting of 3 different consonants
and 2 different vowels?
A.1.64. A has 3 maps and B has 9 maps. Determine the number of
ways in which they can exchange maps if each keeps his initial
number of maps.
A.1.65. In how many ways can a person choose 1 or more of 4
electrical appliances?
A.1.66. In how many ways can 2 or more ties be selected out of 8
ties?
A.1.67. One ball is drawn at random from a box containing 3 red
balls, 2 white balls, and 4 blue balls. Determine the probability p
that it is a) red, b) not red, c) white, d) red or blue.
A.1.68. Determine the probability of throwing a total of 8 in a
single throw with two dice, each of whose faces are numbered from 1
to 6.
A.1.69. The probability of As winning a game of chess against B
is 1/3. What is the probability that A will win at least 1 of a
total of 3 games?
A.1.70. The odds are 23 to 2 against a person winning a $500
prize. What is his mathematical expectation?
A.1.71. A bag contains 6 red, 4 white and 8 blue balls. If 3
balls are drawn at random, determine the probability p that all 3
are red.
A.1.72. A bag contains 6 red, 4 white and 8 blue balls. If 3
balls are drawn at random, determine the probability p that all 3
are blue.
A.1.73. A bag contains 6 red, 4 white and 8 blue balls. If 3
balls are drawn at random, determine the probability p that 2 are
white and 1 is red.
A.1.74. A bag contains 6 red, 4 white and 8 blue balls. If 3
balls are drawn at random, determine the probability p that at
least 1 is red.
A.1.75. A bag contains 6 red, 4 white and 8 blue balls. If 3
balls are drawn at random, determine the probability p that 1 of
each color is drawn.
A.1.76. A bag contains 6 red, 4 white and 8 blue balls. If 3
balls are drawn at random, determine the probability p that the
balls are drawn in the order red, white, and blue.
A.1.77. A box contains 7 tickets, numbered from 1 to 7
inclusive. If 3 tickets are drawn from the box, one at a time,
determine the probability that they are alternately either odd,
even, odd or even, odd, even.
A.1.78. The probability that a certain man will be alive 25
years hence 3/7, and the probability that his wife will be alive 25
years hence 4/5. Determine the probability that, 25 years hence,
both will be alive.
A.1.79. The probability that a certain man will be alive 25
years hence 3/7, and the probability that his wife will be alive 25
years hence 4/5. Determine the probability that, 25 years hence, at
least one of them will be alive.
A.1.80. The probability that a certain man will be alive 25
years hence 3/7, and the probability that his wife will be alive 25
years hence 4/5. Determine the probability that, 25 years hence,
only the man will be alive.
A.1.81.One purse contains 5 dimes and 2 quarters, and a second
purse contains 1 dime and 3 quarters. If a coin is taken from one
of the two purses at random, what is the probability that it is a
quarter?
A.1.82. Eleven books, consisting of 5 engineering books, 4
mathematics books and 2 chemistry books, are placed on a shelf at
random. What is the probability p that the books of each kind are
all together?
A.1.83. One purse contains 6 copper coins and 1 silver coin; a
second purse contains 4 copper coins. Five coins are drawn from the
first purse into the second, and then 2 coins are drawn from the
second and put into the first. Determine the probability that the
silver coin is in a) the second purse, b) the first purse.Ans.: a)
, b)
A.1.84. What is the probability of getting a 9 exactly once in 3
throws with a pair of dice?Ans.: