Download Name: 1. A car rental company charges $45.95 per day, plus $0.35

Name:
1. A car rental company charges $45.95 per day, plus $0.35 per mile. Rachel rented a car for two days and was
charged $117.10. How many miles did Rachel drive the car?
A. 25 miles
C. 117 miles
B. 72 miles
D. 203 miles
2. A rectangular playground has a perimeter of 180 feet. If the width of the playground is 24 feet less than the
length, what is the width, in feet, of the playground?
A. 27
C. 51
B. 33
D. 57
3. Sarah purchased 2 tickets to a movie and a bucket of popcorn. The bucket of popcorn cost $7.00. Sarah paid a
total of $22.00. How much did each movie ticket cost?
A. $4.00
C. $11.00
B. $7.50
D. $14.50
4. The steps used by Kate and Taylor to solve an equation 3(x – 2) = 6(2x + 1) + 6 are shown below:
Kate : 3(x – 2) = 6(2x + 1) + 6
Taylor : 3(x – 2) = 6(2x + 1) + 6
3x – 6 = 12x + 6 + 6
x – 2 = 2(2x + 1) + 2
3x – 6 = 12x + 12
x – 2 = 4x + 2 + 2
-9x – 6 = 12
x – 2 = 4x + 4
-9x = 18
-3x – 2 = 4
x = -2
-3x = 6
x = -2
Part A. List the properties of equality used in each step of the equation on the lines above.
Part B. Did Katie and Taylor both solve the equation correctly? Explain why or why not.
Use words, numbers, and/or pictures to show your work.
5. Martin and his sister started a new tutoring business. They rent an office for $760 per month and charge $120 per
student per month.
Part A: Write an equation to represent the monthly profit they make for tutoring x students.
Part B: If they made a profit of $200 in the first month, solve the equation in part A to find the value of x. Justify
each step by writing the property or reason next to it.
Use words, numbers, and/or pictures to show your work.
6. The steps below are used to solve the equation 5(x – 3) + 2 = 2x – 6.
Step 1: 5x – 15 + 2 = 2x - 6
Step 2: 5x – 13 – 2x = -6
Step 3: 5x – 2x – 13 = -6
Step 4: 3x = -6 + 13
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Step 5: 3x = 7
7
Step 6: 𝑥 = 3
Which of the following statements is correct?
A. Step 1 is the result of applying the associative property of multiplication to the given equation.
B. Step 1 is the result of applying the associative property of addition to the given equation.
C. Step 3 is the result of applying the commutative property to the equation in step 2.
D. Step 3 is the result of applying the distributive property to the equation in step 2.
7. Part A. Solve the equation 2x – 3 = 5 – 2x. Justify each step by listing the property of equality that was used.
Part B. Mathew solved the equation x + 3 = 2x + 9. How is the justification for each step in this equation different
than the equation in part A?
Use words, numbers, and/or pictures to show your work.
8. Which graph best represents the solution to the inequality 2 – 4x ≥ 2x + 20?
A.
B.
C.
D.
9. What is the solution to the equation 5(x – 2) – (x + 3) = x – 8?
A. x = -5
1
B. 𝑥 = − 3
10. Solve:
18𝑥+36
3
= −4(4 − 2𝑥)
26
5
21
−5
C. x = -2
D. x = 14
A. 𝑥 = −
B. 𝑥 =
11. What is the solution to the inequality -31 > 6x + 11?
10
A. 𝑥 > −
B. 𝑥 < −
C. x > -7
D. x < -7
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C. 𝑥 =
3
D. x = 3
3
10
3
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12. What is the value of x when
A.
B.
3
29
15
29
4𝑥
5
=
𝑥+3
?
6
13. What is the solution to the equation
A. –8
B. –7
C.
D.
2𝑥−1
5
3
19
15
19
= −3?
C.
D.
1
5
3
2
14. What value of x satisfies the equation 5(x – 3) – 2(x + 1) = 4?
8
A. 3
B. 3
C. 3
D. 7
15. Which equation is equivalent to 7x – 2 + 4x = 3 + 5x + 7?
A. 3x – 2 = 5x + 10
B. 3x – 2 = 8x + 7
C. 11x – 2 = 5x + 10
D. 11x – 2 = 8x + 7
17
16. Consider the procedure used below to solve the given equation.
Given: 5(2𝑥 − 5) + 2𝑥 + 8 = 43
Step 1: 10𝑥 − 25 + 2𝑥 + 8 = 43
Step 2: 12𝑥 − 17 = 43
Step 3: 12𝑥 = 43 + 17
Step 4: 12𝑥 = 60
Step 5: 𝑥 = 5
Which statement about the solution of the given equation is true?
A. The first mistake was made in Step 1.
C. The first mistake was made in Step 3.
B. The first mistake was made in Step 2.
D. Each step is correct.
17. One of the coldest recorded temperatures in Florida was -2°F Fahrenheit (F) and Celsius (C) temperatures are
related by the formula given below.
9
𝐹 = 𝐶 + 32
5
Which Celsius temperature is closest to a temperature of -2°F
A. -61.2°C
C. -18.9°C
B. -33.1°C
D. -16.7°C
18. In the inequality below, let x represent the number of cakes a bakery makes each day.
5x + 15 ≤ 240
Which phrase most accurately describes the number of cakes the bakery makes each day?
A. less than 45 cakes
C. exactly 45 cakes
B. at most 45 cakes
D. more than 45 cakes
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19. Elias has read 18 pages of a book. He will continue to read at an average rate of 5 page per minute. The total
4
number of pages (p) Elias reads after m minutes can be represented by the equation 𝑝 = 5 𝑚 + 18 How many
minutes will it take Elias to read a total of 39 pages?
A. 13.20 minutes
C. 26.25 minutes
B. 16.80 minutes
D. 30.75 minutes
20. Which equation is equivalent to 5y + 3(2y) + 35 = 103 – y?
A. 5y + 41 = 103 - y
B. 5y + 40 = 103 – y
C. 11y + 35 = 103 - y
D. 16y + 35 = 103 – y
21. When preparing for a 432-mile trip, Luis planned to drive 6 hours, stop for lunch, and then drive for 3 hours more.
𝑚
432−𝑚
If he drives at the same average speed for the entire trip, the equation 6 = 3 can be used to estimate m, the
number of miles he planned to drive before stopping for lunch. How many miles did Luis plan to drive before
lunch?
A. 48
C. 144
B. 72
D. 288
22. What is the value of x in the following equation?
5x – 13 = 15 + 7x
A. -14
B. -1
C. 1
D. 14
23. Which equation is equivalent to 0.4a + 0.1(20 – a) = 3.6?
A. -a + 10 = 3.6
B. -0.6a + 2 = 3.6
C. -0.5a + 10 = 3.6
D. 0.3a + 2 = 3.6
24. Chris uses the equation
to find the total cost, C, in dollars of renting a go-cart for h hours. If Chris does
not spend more than $36, what is the maximum number of hours she can rent the go-cart?
A. 27
C. 10
B. 14
D. 6
25. What is the value of x in the equation –(1 – x) = –2(3x –1)?
1
A. − 7
1
B. − 5
C.
D.
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3
5
3
7
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