Name Ganiera, Dale Vincent CabigasSubject CE Elective 3 ChapterSection CE 5-2Date Submitted January 5, 2015

OBRERO CAMPUSDavao City ALGEBRA

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(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.: