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# Several algebra problems

1. Adult tickets for a play cost \$11 and child tickets cost \$10. If there were 23 people at a performance and the theater collected \$246 from ticket sales, how many children attended the play?

A) 8 children B) 16 children C) 7 children D) 6 children

2. Bob invested \$20,000, part at 14% and part at 13%. If the total interest at the end of the year is \$2,720, how much did he invest at 14%?

A) \$11,000 B) \$12,000 C) \$8,000 D) \$13,000

3. Solve the following system of linear inequalities by graphing.
x - 2y &#61619; 4
x &#61603; 4

A)
B)
C)
D)

4. One number is 12 more than another. The sum of the smaller number and twice the larger number is 39. Find the larger number.

A) 34 B) 17 C) 5 D) 7

5. The length of a rectangle is 8 in. more than twice its width. If the perimeter of the rectangle is 64 in., find the width of the rectangle.

A) 8 in. B) 9 in. C) 10 in. D) 7 in.

6. Solve the following system of linear inequalities by graphing.
x + 2y &#61603; 3
2x - 3y &#61603; 6

A) C)
B) D)

7. Solve the following system of linear inequalities by graphing.
3x + 4y &#61603; 12
x + 3y &#61603; 6
x &#61619; 0
y &#61619; 0

A) C)
B) D)

8. Solve the system by graphing.
3x + y = -1
9x + 3y = -3

A)

---------------------------------------------------------------------------------------------------------
B) There is No Solution

C)

------------------------------------------------------------------------------------------------------
D) Infinitely many solutions (dependent system)

D

9. Solve the system by graphing.
x + y = 4
-x + y = 2

A) Infinitely many solutions (dependent system)
B)
C)
D) None of the above choices

10. Solve the system by addition.
5x - 4y = -5
x - 2y = -7

A) (4, 5)
B) (3, 7)
C) (2, 8)
D) (3, 5)

11. Solve the following system of linear inequalities by graphing.
x - y &#61603; 3
x + 2y &#61619; 6

A)
B)
C)
D)

12. Solve the following system of linear inequalities by graphing.
3x - y < 2
x + y > 2

A)
B)
C)
D)

13. Solve the system by graphing.
3x + y = 6
3x - y = 0

A)
B)
C)
D)

14. Solve the system by graphing.
2x + y = 4
x + y = 3

A)
B)
C)
D)

15. A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities.

A) 2x + 14y &#61603; 40
x + y &#61603; 5
x &#61619; 0
y &#61619; 0

B)
C)
D) None of the above Choices

16. Angus invested \$18,000, part at 3% and part at 5%. If the total interest at the end of the year is \$660, how much did he invest at each rate?

A) \$13,500 at 3% and \$4,500 at 5%
B) \$12,000 at 2.5% and \$6,000 at 6.9%
C) \$11,000 at 4% and \$7,000 at 5.5%
D) \$12,000 at 3% and \$6,000 at 5%

17. Solve the system by addition.
2x - 4y = 7
4x + 2y = 9

A)

B)

C)

D)

18. Solve the following system of linear inequalities by graphing.
x - 3y > 6
3x + 2y > 12

A)
B)
C)
D)

19. Sally bought three chocolate bars and a pack of gum and paid \$1.75. Jake bought two chocolate bars and four packs of gum and paid \$2.00. Find the cost of a chocolate bar and the cost of a pack of gum.

A) Chocolate 55¢, gum 35¢
B) Chocolate 65¢, gum 45¢
C) Chocolate 75¢, gum 15¢
D) Chocolate 50¢, gum 25¢

20. Solve the system by graphing.
x + y = 3
x + y = -1

A) No solution (inconsistent system)

B)
C) This System has many Solutions
D) None of the above Choices are correct

#### Solution Summary

Step by step solutions to all the problems are provided.

\$2.19