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Algebra / Statistics (50 Problems) : Sets, Word Problems and Systems of Inequalities and Equations

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1. Convert 0.58 to a fraction and write your answer in lowest terms.

2. Evaluate. | 16 | - | -11 |
A) -27
B) -5
C) 5
D) 27

3. Simplify: -(-(-27)).

4. Determine the maximum and minimum values for the following set.
5, -50, 30, 20, -18, -6

5. Express 76% as a fraction.

6. Subtract. 14.318 - 10.72

7. Find the opposite of 44.

8. List all the factors of 16.

9. Which property of the real numbers is illustrated by the following statement?
19 + 3 = 3 + 19
A) Commutative property of addition
B) Associative property of addition
C) Distributive property

10. Which of the following is not an expression?
A) a(t + 9)
B) a - ÷ t
C) t?a - 3
D) t + a + 6

11. Marcie gets paid $1.25 an hour to babysit her little brother. If she babysits for 3 hours, how much money do Marcie's parents owe her?
A) $3.25
B) $3.50
C) $3.75
D) $4.00

12. Evaluate b2 - 2bc + c2 if b = 3 and c = -2.
A) -7
B) 1
C) 17
D) 25

13. Multiply.
a6 a8

14. Use the distributive property to remove the parentheses in the following expression. Then simplify your result if possible.

A) 21
B) 9
C) 20
D) 10

15. Use the properties of addition and multiplication to complete the statement.
12 ? (17 + 4) = 12 ? ____ + 12 ? 4

16. Subtract. -20 - 18
A) 38
B) 2
C) -2
D) -38

17. Solve. 10x - 4 - 5x = 6 + 3x - 8

18. A home purchased for $300,000 depreciated 8% over a 1-year period. What was the value of the home after at the end of the year?
A) $272,000
B) $274,000
C) $276,000
D) $278,000

19. Find the mean and the median.
-7, -6, 1, 9, 10, 17

20. Solve. -6(x + 3) - 10 = 3(-2x - 5) - 13

21. Find the mean.
3, 5, 7, 12, 13

22. Solve. -5(x + 5) = -10

23. Solve for b. a = bc2

A)

B)

C)

D)

24. Solve. 6(2 - x) = 4x

25. The line graph below shows the number of trees in a certain seaside town.

(a) Which year had the fewest trees?
(b) Between which two years did the greatest increase in the number of trees occur?

26. If y varies directly with x, and y = 42 when x = 3, find the constant of variation k.

27. Find the slope of the line passing through the points (1, -3) and (-9, 0).
A)

B)

C)

D)

28. Graph 3x + 2y = 6.
A)

B)

C)

D)

29. Find the slope of the line passing through the points (8, 8) and (7, 7).

30. The following bar graph shows the enrollment at a community college.

How many people were enrolled in 1998?

31. The following bar graph shows the enrollment at a community college.

What was the increase in enrollment from 1999 to 2000?

32. Which of the ordered pairs is a solution for the equation 2x - 3y = 6?
A) (0, 2)
B) (-3, 0)
C) (-3, -2)
D) (0, -2)

33. Find the slope of the graphed line.

A) 4
B) -4
C)

D)

34. Graph f(x) = 4x + 1.

35. Rewrite the equation -x - 2y = 20 as a function of x.

36. Write the equation of the line that passes through point (2, -2) with a slope of 3.

37. Match the graph with one of the equations.

A) y = x

B) y = 3x
C) y =

D) y = x + 3

38. Write the equation of the line with slope -2 and y-intercept (0, 0). Then graph the line.
A) y = -2x

B) y = -2x

C) y = x - 2

D) y = x - 2

39. Graph the inequality.
x - y  2

40. Are the following lines parallel, perpendicular, or neither?
L1 through (-4, -7) and (1, 3)
L2 through (2, 6) and (4, 10)
A) Parallel
B) Perpendicular
C) Neither

41. Graph f(x) = -2x + 4.

42. Find the y-intercept.
-x - 9y = -9
A) (9, 0)
B) (0, 1)
C) (1, 0)
D) (0, 9)

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

44. Solve the system by graphing.
3x - y = 1
3x - y = 2

45. The difference of two numbers is 68. The second is 8 less than 5 times the first. What are the two numbers?

46. Solve the system by graphing.
x - y = -3
x - y = 4

47. Solve the system by graphing.
x - y = 2
3x - 3y = 6

48. Solve the system by substitution.
4x + 3y = 12
y = -x + 5

49. Solve the system by addition or substitution.
-10x + 5y = -36
y = 2x - 8

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

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Fifty algebra problems are solved and explained.

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Systems of Equations and Inequalities Word Problems

Statistics. After reading an article on the front page of The New York Times titled "You Have to Be Good at Algebra to Figure Out the Best Deal for Long Distance," Rafaella De La Cruz decided to apply her skills in algebra to try to decide between two competing long-distance companies. It was difficult at first to get the companies to explain their charge policies. They both kept repeating that they were 25% cheaper than their competition. Finally, Rafaella found someone who explained that the charge depended on when she called, where she called, how long she talked, and how often she called. "Too many variables!" she exclaimed. So she decided to ask one company what they charged as a base amount, just for using the service.

Company A said that they charged $5 for the privilege of using their long distance service, whether or not she made any phone calls, and that because of this fee they were able to allow her to call anywhere in the United States after 6 P.M. for only $0.15 a minute. Complete this table of charges based on this company's plan: Use this table to make a graph of the monthly charges from Company A based on the number of minutes of long distance.

Rafaella wanted to compare this offer to Company B, which she was currently using. She looked at her phone bill and saw that one month she had been charged $7.50 for 30 minutes and another month she had been charged $11.25 for 45 minutes of long-distance calling. These calls were made after 6 P.M. to her relatives in Indiana and Arizona. Draw a graph on the same set of axes you made for Company A's figures. Use your graph and what you know about linear inequalities to advise Rafaella about which company is best.

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