1. A recycling center pays $0. 35 per pound of glass that it receives
A recycling center pays $0.35 per pound of glass that it receives. If students at Falcon High School want to raise $500 in a glass-recycling project, what is a reasonable number of pounds of glass they must collect?
A 750 lb
B 175 lb
C 500 lb
D lb
Problem #1
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2. A weather balloon is launched from a height of 475 feet above sea level. If the balloon rises at a constant rate of 85 feet per minute, which equation could be used to determine t, the time in minutes it will take the balloon to reach a height of 9245 feet above sea level?
A = t
B = 85(t + 475)
C = t
D = ( )t
Problem #2
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3. If (x, –4) is a solution to the equation 4x – 5y = 8, what is the value of x?
B –3
C 1.6
D 7
Problem #3
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4. The graphs of the linear equations y = 2x – 3 and
y = 3x – 7 are shown to the right.
If 2x – 3 = 3x – 7, what is the value of x?
A 4
B 5
C 9
D 10
Problem #4
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5. A shaded parallelogram is graphed on the coordinate grid to the right.
Which of the following functions describes a line that would include an edge of the shaded parallelogram?
A y = –2x + 5
B y = –2x – 2
C y = –2x + 9
D y = –2x – 1
Problem #5
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6. What is the x-coordinate of the solution to the system of linear equations below?
4x + 5y = 8
2x – 3y = –18
A –4
B –3
C 3
D 4
Problem #6
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7. In 1998 the enrollment at a community college was approximately 2500 students. In 2002 the enrollment had increased to 3250 students. If the enrollment continues to increase at this rate, what is a reasonable projection of enrollment for 2010?
A 4750
B 5750
C 6250
D 9000
Problem #7
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8. Chase and Sara went to the candy store
Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of $3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?
A 5f + 3g = 3.60
2f + 10g = 5.70
B 5f + 2g = 5.70
3f + 10g = 3.60
C f + g = 22
7f + 13g = 9.30
D 5f + 3g = 5.70
2f + 10g = 3.60
Problem #8
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9. Rita put some hummingbird feeders in her backyard
Rita put some hummingbird feeders in her backyard. The table shows the number of hummingbirds that Rita saw compared to the number of feeders.
Which equation best describes the relationship between h, the number of hummingbirds, and f, the number of feeders?
A h = 2f + 1
B f = 2h + 1
C h = f + 2 D
Problem #9
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10. The graph of the equation is given to the right. Graph
y = x + 1 on the grid.
What is the solution to this system of equations?
A (0, 1)
B (5, 6)
C (6, 7)
D No solution
Problem #10
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11. At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, m, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?
A m + n = 8
m = 3n + 54
B m + n = 8
m = 3n – 54
C m + n = 54
m = 3n+ 8
D m + n = 54
m = 3n – 8
Problem #11
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12. The amount of an employee’s weekly pay, p, including a bonus, can be represented by the inequality
6.00h < p < 6.50h + 125, where h represents the number of hours worked by the employee. If an employee worked 25 hours, which of the following is a reasonable amount for that week’s pay?
A $118.75
B $250.00
C $272.50
D $290.25
Problem #12
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13. The price, e, of an entertainment system at Extreme Electronics is $220 less than twice the price, u, of the same system at Ultra Electronics. The difference in price between the system at Extreme Electronics and Ultra Electronics is $175. Which system of linear equations can be used to determine the price of the system at each store?
A 2e – u = 220
e – u = –175
B 2e – u = 220
e + u = 175
C 2e – 2u = 440
D e – 2u = –220
e – u = 175
Problem #13
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14. Ms. Barton determined that the total cost of her wedding, c, could be represented by the equation c = 75n , where n is the number of people attending the wedding. If Ms. Barton’s wedding cost $8625, how many people attended the wedding?
A 135
B 95
C 115
D 75
Problem #14
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15. Auto-Check Motors charged Mr. Jones $84
Auto-Check Motors charged Mr. Jones $84.00 for an automotive part plus $68.00 per hour that a mechanic worked to install the part. The total charge was $ For about how long did the mechanic work to install the part on Mr. Jones’s car?
A. 6 hours
B. 5 hours
C. 4 hours
D. 3 hours
Problem #15
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16. The number of hours Abe practices golf each week, g, is 2 more than the number of hours he runs, r. Which equation represents the number of hours he runs each week?
A. r = g – 2
B. g = r – 2
C. g = 2r
D. r = g + 2
Problem #16
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17. Ms. Kitts works at a music store
Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 108 CDs over the two weeks. Which system of equations can be used to find l, the number of CDs she sold last week, and t, the number of CDs she sold this week?
A. l + t = 108
t = 3l + 6
B. l + t = 108
t = 3l – t
C. l + t = 108
l = 3t – 6
D. l + t = 108
l = 3t + 6
Problem #17
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18. The cost of renting a DVD at a certain store is described by the function
f(x) = 4x + 3
in which f(x) is the cost and x is the time in days. If Lupe has $12 to spend, what is the maximum number of days that she can rent a single DVD if tax is not considered?
A. 1
B. 2
C. 3
D. 7
Problem #18
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19. Passengers on many commercial flights may make calls from a telephone provided by the airline. On a certain airline a call costs $3 to connect plus $2 for each minute. Which equation best represents c, the total cost for a call that lasts m minutes?
A. m = 3 + 2c
B. c = 3 + 2m
C. m = 2 + 3c
D. c = 2 + 3m
Problem #19
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20. At Northwest Electronics audiotapes cost $5
At Northwest Electronics audiotapes cost $5.00 per package, and videotapes cost $10.00 per package. Which inequality best describes the number of packages of audiotapes, a, and the number of videotapes, v, that can be purchased for $45.00 or less?
A. 5a + 10v < 45
B. 10a + 5v ≤ 45
C. 5a + 10v ≤ 45
D. 10a + 5v < 45
Problem #20
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21. The length of a rectangle is equal to triple the width
The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 85 centimeters?
A. l = w + 3
2(l + w) = 85
B. l = 3w
2l + 6w = 85
C. l = 3w
D. l = w + 3
Problem #21
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22. What is the value of y if (3, y) is a solution to the equation 5x – 3y = 18?
B. 1
C. –1
D. –11
Problem #22
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23. Marcos had 15 coins in nickels and quarters
Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a systems of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. Then he solved the system by graphing. What is the solution?
A. (6, 9)
B. (5, 10)
C. (9, 6)
D. (10, 5)
Problem #23
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24. Which graph best represents a solution to this system of equations?
2x – 3y = 0
x + 2y = –7
Problem #24
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25. At a restaurant the cost for a breakfast taco and a small glass of milk is $2.10. The cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?
A. t + m = 2.10
2t + 2m = 5.15
B. t + m = 2.10
3t + 3m = 5.15
C. t + m = 2.10
3t + 2m = 5.15
D. t + m = 2.10
2t + 3m = 5.15
Problem #25
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26. Anna makes hand-painted plates
Anna makes hand-painted plates. Her overhead costs are $750 per week, and she pays an additional $10 per plate in material costs. If Anna sells the plates for $25 each, how many plates does she have to sell each week before she can make a profit?
A. 20
B. 30
C. 50
D. 75
Problem #26
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27. At a firefighters’ pancake breakfast, the firefighters served 345 people and raised $1395. If the cost of a, an adult’s ticket to the pancake breakfast, was $5 and the cost of c, a child’s ticket, was $3, what was the number of adult tickets sold?
A. 165
B. 180
C. 279
D. 345
Problem #27
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28. On Wednesdays an athlete’s schedule allows no more than 75 minutes for morning training. One round of a strength routine, s, requires 8 minutes. One round of an endurance routine, e, requires 12 minutes. Which of these best represents the time available for the athlete to spend on strength and endurance routines on Wednesdays?
A. 20(s + e) > 75
B. 8s = 75 – 12e
C. 8s + 12e ≤ 75
D. 12e < s
Problem #28
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29. Valerie purchased x tubes of lipstick at $4 each and y bottles of nail polish at $2 each. She spent less than $12, not including tax. Use the grid to the right to graph the inequality 4x + 2y < 12.
Which point represents a reasonable number of lipsticks and bottles of nail polish that Valerie purchased?
A. (1, 5)
B. (2, 3)
C. (1, 3)
D. (2, 2)
Problem #29
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30. If (x, −3.2) is a solution to the equation 4x = 5y − 17, what is the value of x?G
H. −5.96
J. −8.25
Problem #30
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31. Harris has $20.92 to spend on video-game rentals at a local video store. The store charges $3.95 per video-game rental plus an 8.125% tax. What is the maximum number of video games that Harris can rent?
A. 5
B. 4
C. 6
D. 3
Problem #31
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32. The perimeter of a rectangular wooden deck is 90 feet
The perimeter of a rectangular wooden deck is 90 feet. The deck’s length, l , is 5 feet less than 4 times its width, w. Which system of linear equations can be used to determine the dimensions, in feet, of the wooden deck?
F. 2l + 2w = 90
l = 5 – 4w
G. 2l + 2w = 90
l = 5w – 4
H. 2l + 2w = 90
l = 4 – 5w
J. 2l + 2w = 90
l = 4w – 5
Problem #32
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33. Brandon has a budget of $58 to spend on clothes
Brandon has a budget of $58 to spend on clothes. The shirts he wants to buy are on sale for $9 each, and the pair of pants he wants costs $21. All prices include tax. Which inequality could be used to determine s, the maximum number of shirts Brandon can buy if he also buys the pair of pants?
F. 21s + 9 < 58
G. 9s
H. 30s < 58
J. 9s −
Problem #33
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34. A florist plans to sell bouquets for $25 each. He wants to use only
roses and carnations in each bouquet and needs to charge the
following amount for each type of flower.
$1.50 per rose
$1.25 per carnation
Which of these combinations of roses and carnations will result
in bouquets that the florist can sell for exactly $25 each?
I. 18 roses and 2 carnations
II. 6 roses and 10 carnations
III. 10 roses and 8 carnations
IV. 5 roses and 14 carnations
F. I and II only
G. II and III only
H. III and IV only
J. I and IV only
Problem #34
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35. In 2004 a married couple could have calculated their estimated income tax, t, for that year using the equation
t = 0.25c − 6525, in which c represents their combined taxable income. If a married couple had a combined taxable income between $60,000 and $64,000, which of the following is a reasonable amount for their income tax?
F. $6,525
G. $8,975
H. $13,869
J. $15,500
Problem #35
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36. Norma and Lauretta went to a store to buy DVDs on sale
for $5 each, tax included. Norma purchased two and a half
times as many DVDs as Lauretta purchased. Together they
purchased 14 DVDs. Which system of linear equations can
be used to determine n, the number of DVDs Norma purchased, and l, the number of DVDs Lauretta purchased?
n + l = 14
n = ½ l
G. 5n + 5l = 14
l = ½ n
H. n + l = 14
n = l
J. n + l = 14
l = n
Problem #36
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37. The length of each leg of an isosceles triangle is 5 centimeters more than twice the length of the base. If the perimeter of this isosceles triangle is 95 centimeters, what is the length of the base?
A. 17 cm
B. 21 cm
C. 30 cm
D. 39 cm
Problem #37
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38. If the system of linear equations 2x + y = 1 and y = − ½ x + 1
are graphed on the same coordinate grid, which of the following is the solution to this system of linear equations?
A. (2, 0)
B. (0, 2)
C. (0.5, 0)
D. Not here
Problem #38
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39. A chemist started an experiment with 5 grams of a chemical.
The chemical was used at a rate of 0.01 gram per minute.
Which equation best describes the relationship between c, the amount of chemical remaining in grams, and t, the time in minutes?
F. c = 5.01t
G. c = 4.99t
H. c = 5 − 0.01t
J. c = 0.01t − 5
Problem #39
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40. The student council at Jefferson High School sold a total
of 220 brownies and cookies during its fund-raiser. Each
brownie sold for $0.75, and each cookie sold for $0.50.
The student council made $ from the sales of brownies
and cookies. Which system of linear equations can be used
to find b, the number of brownies sold, and c, the number
of cookies sold?
A. b + c = 220
0.50b c =
B. b + c =
0.75b c = 220
C. b + c =
0.50b c = 220
D. b + c = 220
0.75b c =
Problem #40
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41. A salesclerk earns $250 per week plus a commission of of
her total sales. If her sales total x dollars, which equation
can be used to determine her total weekly earnings?
A. y = 250(x + )
B. y = 250x + x
C. y = 250x +
D. y = x
Problem #41
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42. The equation F = C + 32 represents the relationship between F, the temperature in degrees Fahrenheit, and C, the temperature in degrees Celsius. If the temperature is 104°F, what is the temperature in degrees Celsius?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
Problem #42
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43. The graph of a system of linear equations is shown below.
Which of the following is the solution to this system of linear equations?
F. (0, 4)
G. (8, 1)
H. (0, −3)
J. (10, 2)
Problem #43
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44. Lisa wants to make a long-distance telephone call to her friend
Lisa wants to make a long-distance telephone call to her friend. She does not want to spend more than $5.00 on the telephone call. If there is a $0.50 connection fee and a charge of $0.11 per minute, which best represents the number of minutes that Lisa can talk to her friend? A. B. C. D.
Problem #44
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