beginning and intermediate algebra chapter...

BEGINNING and INTERMEDIATE ALGEBRA

55

CHAPTER 2, FORM A NAME_____________________________ SECTION_____________________ For Exercises 1-5, solve the equation. 1. 7496 −=− xx 1. ___________________

2. 284

7 =− p 2. ___________________

3. jjj 273)4(3 +=+−− 3. ___________________ 4. 25)40(7.0)70(3.0 ++=+ ww 4. ___________________ 5. 63)13()2(5 −=−−− ddd 5. ___________________ For Exercises 6-7, solve the problem. 6. A log 78 feet long is to be cut into three pieces of varying lengths. The longest piece is to be four times the length of the shortest piece and the middle-sized piece is to be 6 feet less than twice the length of the shortest piece. How long is the shortest piece? 6. ___________________ 7. If 7 times a number is added to 18, the result is –17. Find the number. 7. ___________________ 8. Find the measure of an angle if its supplement measures 15 less than four times its complement. 8. ___________________

9. The formula for the area of a trapezoid is ( )hbBA +=2

1.

(a) Solve for b. 9. (a) _________________ (b) If 8 and,5,80 === hBA , find the value of b. (b) _________________

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CHAPTER 2, FORM A

56

For Exercise 10, find the measure of each marked angle. 10. )2015( +x )617( +x 10.__________________

11. Suppose that in the equation d

c

b

a = , a and b are positive

numbers and d is a negative number. Must c be positive or negative? 11. __________________

12. Solve the equation 5 4

.5 8

x x+ −= 12. __________________

For Exercises 13-16, solve the problem. 13. If 11 gallons of gasoline cost $13.86, find the cost of 13 gallons of gasoline. 13. __________________ 14. The distance between Buffalo, New York and Chicago, Illinois is 600 miles. On a U.S. road atlas, this distance is represented by 10 inches. On the same atlas, the distance between Chicago and Denver, Colorado is 18 inches. What is the distance between Chicago and Denver? 14. __________________ 15. Two investments produce a total annual interest income of $201. If $1200 more was invested at 7% than at 6%, how much was invested at 6%? 15. __________________ 16. Kate has $780 in five-dollar bills and twenty-dollar bills. If she has four more twenties than fives, how many five- dollar bills does she have? 16. __________________


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CHAPTER 2, FORM A

57

For Exercises 17-19, solve the inequality and graph the solution. 17. www −−−≥−− )7(33)5(6 17. __________________

18. 15363 ≤−≤− y 18. __________________

19. 962

33 <+<− x 19. __________________

20. John Maxwell has grades of 84 and 90 on his first two Biology tests. What possible scores could he make on his third test so that his average is at least 88? 20. __________________




59

CHAPTER 2, FORM B NAME_____________________________ SECTION_____________________ For Exercises 1-5, solve the equation. 1. 13148 −=+ xx 1. ___________________ 2. )3(22)54(6 dd +−=− 2. ___________________ 3. yy −=+− 8)2(6 3. ___________________

4. 205

4 −=x 4. ___________________

5. 6.7)30(06.0)10(04.0 =−++ kk 5. ___________________ For Exercises 6-7, solve the problem. 6. If 8 is subtracted from five times a number, the result is 2 more than six times the number. Find the number. 6. ___________________ 7. A ribbon 106 inches long is cut into three pieces. The middle-sized piece is 4 inches longer than twice the shortest piece. The longest piece is 3 times as long as the shortest piece. How long is the shortest piece? 7.___________________ 8. Find the measure of an angle if its supplement measures 30 more than twice its complement. 8. ___________________ 9. A formula for an equation of a straight line is bmxy += . (a) Solve for m. 9. (a) ________________ (b) If 3 and,15,3 −=== xby , find the value of m. (b) ________________



CHAPTER 2, FORM B

60

For Exercise 10, find the measure of each marked angle. 10. )137( +x )28( −x 10. __________________

11. Suppose that in the equation d

c

b

a = , a and d are negative

numbers and c is a positive number. Must b be positive or negative? 11. __________________


.7 8

x x− −= 12. __________________

For Exercises 13-16, solve the problem. 13. If 11 gallons of gasoline cost $12.21, find the cost of 19 gallons of gasoline. 13. __________________ 14. How many gallons of a 25% chemical solution must be added to 60 gallons of a 50% solution to get a 30% solution? 14. __________________ 15. Two trains leave Houston at the same time. One travels west at 70 miles per hour and the other travels east at 65 miles per hour. In how many hours will they be 1215 miles apart? 15. __________________ 16. Rachel invested a certain amount of money at 9% and $800 more at 11% The annual interest that she earned was $188. How much did she invest at 11%? 16. __________________



CHAPTER 2, FORM B

61

For Exercises 17-19, solve the inequality and graph the solution. 17. ppp 7)2(4)2(34 −−<++ 17. __________________

18. 15176 <+≤− y 18. __________________

19. 735

25 <+< t 19. __________________

20. Steve Smith worked 7 hours on Wednesday and 9 hours on Thursday. What are the possible numbers of hours she can work on Friday to average at least 7 hours per day for those three days? 20. __________________




63

CHAPTER 2, FORM C NAME_____________________________ SECTION_____________________ For Exercises 1-5, solve the equation. 1. 8732 −=− xx 1. ___________________ 2. )10(252)5(3 −++−=+ aaa 2. ___________________ 3. rrr 53)13(34 −=−− 3. ___________________

4. 105

4 −=n 4. ___________________

5. 57)20(7.0)10(5.0 =++− xx 5. ___________________ For Exercises 6-7, solve the problem. 6. If 3 is subtracted from four times a number, the result is 10 less than five times the number. Find the number. 6. ___________________ 7. During the 1987-88 NBA season, Michael Jordan scored 92 points fewer than twice the number of points Brad Daugherty scored. Larry Bird scored 795 more points than Daugherty. Altogether, the three players scored 6623 points. How many points did Daugherty score? 7. ___________________ 8. The sum of the measures of the complement and supplement of an angle is 196 . Find the measure of the angle. 8. ___________________

9. The formula for the area of a triangle is bhA2

1= .

(a) Solve for h. 9. (a) ________________ (b) If 40 and140 == bA , find the value of h. (b) ________________



CHAPTER 2, FORM C

64

For Exercise 10, find the measure of each marked angle. 10. )108( −x )107( +x 10. __________________ For Exercises 11-12, solve each proportion.

11. 27

8 24

y = 11. __________________

12. 3

12

4

32 +=+ ss 12. __________________

For Exercises 13-16, solve the problem. 13. If 7 quarts of ice cream cost $19.53, find the cost of 12 quarts of ice cream. 13. __________________ 14. Two planes leave Chicago’s O’Hare airport at the same time One flies east to Washington, D.C. at 550 miles per hour. The other flies west to Las Vegas, Nevada at 475 miles per hour. In how many hours will they be 2050 miles apart? 14. __________________ 15. Brad has $700 in ten-dollar bills and twenty-dollar bills. If he has two more twenties than tens, how many twenty-dollar bills does he have? 15. __________________ 16. Whitney receives $147 annual interest income on two investments. If the amount she invested at 6% was $350 more than the amount she invested at 8%, how much did she invest at 6%? 16. __________________



CHAPTER 2, FORM C

65

For Exercises 17-19, solve the inequality and graph the solution. 17. )52(54)5(69 −−−>−+− qqqq 17. __________________

18. 9743 <−≤− r 18. __________________

19. 484

31 <−< t 19. __________________

20. Gail Brown earned $331 and $296 the first two weeks that she worked as a caterer. What are the possible amounts she can earn the third week in order to average at least $325 per week? 20. __________________




67

CHAPTER 2, FORM D NAME_____________________________ SECTION_____________________ For Exercises 1-5, solve the equation. 1. 198115 −=+ aa 1. ___________________ 2. )4(2)1(53 −+=+− zz 2. ___________________ 3. 7374)7( −=−++− ddd 3. ___________________

4. 26

5 =− n 4. ___________________

5. 32)20(6.0)20(2.0 =++− xx 5. ___________________ For Exercises 6-7, solve the problem. 6. If a number is subtracted from 94, the result is 19 more than –5. Find the number. 6. ___________________ 7. Diane ordered 474 costumes for her church Easter pageant. She ordered 56 more costumes from Castle Company than from Ajax Costumes. She ordered 42 fewer costumes from Light Fantastic than 3 times the number from Ajax. How many costumes did she order from Ajax? 7. ___________________ 8. Find the measure of an angle if its supplement measures 4 less than three times its complement. 8. ___________________

9. The formula for the area of a trapezoid is hbBA )(2

1 += .

(a) Solve for b. 9. (a) ________________ (b) If 12 and,43,240 === hBA , find the value of b. (b) ________________



68 CHAPTER 2, FORM D

For Exercise 10, find the measure of each marked angle. 10. )183( +x )114( +x 10. __________________ For Exercises 11-12, solve each proportion.

11. 7 28

36x= 11. __________________

12. 2

5

7

8 =−+

s

s 12. __________________

For Exercises 13-16, solve the problem. 13. If 4 quarts of ice cream cost $10.76, find the cost of 11 quarts of ice cream. 13. __________________ 14. How many gallons of 70% antifreeze must be mixed with 120 gallons of 20% antifreeze to get a mixture that is 40% antifreeze? 14. __________________ 15. Two planes leave New York’s Kennedy airport at the same time. One flies east to Paris, France at 550 miles per hour. The other flies west to Tokyo, Japan at 475 miles per hour. In how many hours will they be 7175 miles apart? 15. __________________ 16. Two investments produce annual interest income of $270. If the amount invested at 9% was $800 more than the amount invested at 7.5%, how much was invested at 9%? 16. __________________



CHAPTER 2, FORM D

69

For Exercises 17-19, solve the inequality and graph the solution. 17. )1(84)45(210 +−≥−−− bbb 17. __________________

18. 144913 <−≤− c 18. __________________

19. 153

17 <−<− t 19. __________________

20. Steve Buchelt sold his first two professional photographs for $190 and $215. What are the possible amounts he can charge for his third photograph in order to average at least $200 per photograph? 20. __________________




71

CHAPTER 2, FORM E NAME_____________________________ SECTION_______________________ For Exercises 1-5, solve the equation. 1. 28126 +=+ xx

(a) 5− (b) 5 (c) 1− (d) 1 1. _________ 2. 9)515()12(43 =−−−++ yyy

(a) 6

1− (b) 6

19 (c) 19 (d) 6 2. _________

3. 606

5 −=m

(a) 72− (b) 72 (c) 50− (d) 50 3. _________

4. 21)10(9.0)20(3.0 =−++ xx

(a) 20 (b) 10−

(c) All real numbers (d) No solution 4. _________ 5. )5()7(2 kk +−−=−+−

(a) 5 (b) 0

(c) All real numbers (d) No solution 5. _________ For Exercises 6-7, solve the problem. 6. The difference between 2 times a number and –8 is –12. Find the number. (a) 2 (b) –2 (c) 10 (d) –10 6. _________ 7. A 36-foot pipe is divided into three pieces. One piece is twice as long as the shortest piece, and the third piece is 1 foot longer than four times the shortest piece. Find the length of the shortest piece.

(a) 10 feet (b) 21 feet

(c) 5 feet (d) 4 feet 7. _________



72 CHAPTER 2, FORM E

8. The measure of the supplement of an angle is 4 times the measure of its complement. Find the measure of the angle. (a) 40 (b) 45

(c) 50 (d) 60 8. _________ 9. The formula for the perimeter of a rectangle is WLP 22 += . If 20 and 110 == LP , find the value of W.

(a) 35 (b) 45 (c) 70 (d) 90 9. _________

10. Solve the formula bhA2

1= for b.

(a) h

Ab

2= (b) Ahb 2=

(c) hAb −= 2 (d) A

hb

2= 10. ________

For Exercise 11, find the measure of each marked angle. 11. )104( −x )103( +x (a) 20,20 (b) 70,70

(c) 40,40 (d) 30,30 11. ________


.9 3

x

x

+=

−

(a) 9− (b) 42− (c) 43 (d) 6 12. ________

For Exercises 13-16, solve the problem. 13. If 8 boxes of tissue cost $10.00, how much will 15 boxes of tissue cost?

(a) $15.00 (b) $18.75

(c) $19.75 (d) $18.40 13. ________



CHAPTER 2, FORM E

73

14. Andrew invested some of his money at 7.5% and $350 less at 8%. His total annual interest income is $437. How much did Andrew invest at 7.5%?

(a) $2988.71 (b) $3000

(c) $2650 (d) $8215 14. ________ 15. How many liters of pure acid must be mixed with 20 liters of a 15% acid solution to get a 20% mixture?

(a) 10 liters (b) 12.5 liters

(c) 100 liters (d) 1.25 liters 15. ________ 16. Kelly has a purse full of quarters and dimes. There are 58 more quarters than dimes and the total value of the change is $19.05. How many dimes are there?

(a) 71 (b) 13 (c) 129 (d) 20 16. ________ For Exercises 17-19, determine the graph of the solution of the inequality. 17. 16)12(410)43(5 −−≤−− xxx 17. ________ (a) (b)

(c) (d)

18. 8624 <−≤− b 18. ________

(a) (b)

(c) (d)



74 CHAPTER 2, FORM E

19. 132

15 −<−<− x 19. ________

(a) (b)

(c) (d)

20. If yy 23 < , then

(a) y may be positive or negative (b) y must be zero (c) y must be positive (d) y must be negative 20. ________




75

CHAPTER 2, FORM F NAME_____________________________ SECTION________________________ For Exercises 1-5, solve the equation. 1. 159117 +=+ xx

(a) 2 (b) –2 (c) 4

1− (d) 8

13 1. _________

2. 9)393()23(22 =−−−++ aaa

(a) 11

7− (b) 5

7− (c) 5

17 (d) 7− 2. _________

3. 205

2 −=m

(a) –50 (b) 50 (c) –8 (d) 8 3. _________

4. )10(13)3( +−=−− xx

(a) 0 (b) 6

(c) All real numbers (d) No solution 4. _________ 5. 8.10)10(27.0)30(06.0 =++− xx

(a) 30 (b) 3

(c) All real numbers (d) No solution 5. _________

For Exercises 6-7, solve the problem. 6. If 5 is subtracted from three times a number, the result is 7 more than twice the number. What is the number? (a) 2 (b) –2 (c) 12 (d) –12 6. _________ 7. A 60-foot pipe is divided into three pieces. One piece is twice as long as the shortest piece, and the third piece is 4 feet less than five times the shortest piece. Find the length of the shortest piece. (a) 8 feet (b) 7 feet (c) 6 feet (d) 4 feet 7. _________



76 CHAPTER 2, FORM F

8. Find the measure of an angle if its supplement measures 10 less than three times its complement.

(a) 40 (b) 140

(c) 50 (d) 60 8. _________ 9. A formula for an equation of a straight line is bmxy += . If 3 and4,m31, −==−= by , find the value of x.

(a) –7 (b) 7 (c) –9 (d) 9 9. _________

10. Solve the formula hrV 2

3

1 π= for h.

(a) V

rh

3

2π= (b) 2

3

1rVh π−=

(c) 2

3

r

Vh

π= (d)

2

3

Vrh

π= 10. ________

For Exercise 11, find the measure of each marked angle. 11. )24( +x )135( −x

(a) 62,62 (b) 19,19

(c) 28,28 (d) 118,118 11. ________


.8 5

w w+ +=

(a) 2− (b) 2 (c) 20− (d) 3

22− 12. ________



CHAPTER 2, FORM F

77

For Exercises 13-16, solve the problem. 13. If 9 boxes of tissue cost $11.25, how much will 16 boxes of tissue cost?

(a) $21.25 (b) $20.00

(c) $19.50 (d) $20.25 13. ________ 14. Matthew invested some of his money at 6.5% and $450 less at 8%. His total annual interest income is $167. How much did Matthew invest at 8%?

(a) $1400 (b) $1850

(c) $950 (d) $500 14. ________ 15. Jason has a pocket full of quarters and dimes. There are 58 more quarters than dimes and the total value of the change is $20.45. How many dimes are there?

(a) 75 (b) 17 (c) 58 (d) 34 15. ________ 16. Two cars leave from the same point, traveling in opposite directions. If one travels at a constant speed of 52 miles per hour and the other travels at a constant speed of 58 miles per hour, in how many hours will they be 385 miles apart?

(a) 3 hours (b) 4 hours (c) 2

13 hours (d)

2

14 hours 16. ________

For Exercises 17-19, determine the graph of the solution of the inequality. 17. eee 8)13(48)3(7 −−≥+− 17. ________

(a) (b)

(c) (d)



78 CHAPTER 2, FORM F

18. 18352 <+≤− q 18. ________

(a) (b)

(c) (d)

19. 143

12 −<−<− g 19. ________

(a) (b)

(c) (d)

20. If pp 95 −>− , then

(a) p must be positive or negative (b) p must be zero (c) p must be positive (d) p must be negative 20. ________



beginning and intermediate algebra chapter...

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