College

**Question 1 (5 points)**

Determine which expression is equivalent to \(15a + 6\).

A. \(3(5a + 6)\)
B. \(3(5a + 2)\)
C. \(5(3a + 6)\)
D. \(5(3a + 2)\)

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**Question 2 (5 points)**

Excellence Middle School charges $6.25 for students from all grade levels to attend the school dance. If \(s\) represents the number of seventh grade students who came to the dance and \(g\) represents the number of eighth grade students at the dance, which expression best represents the total money collected for attending the dance?

A. \(6.25s + g\)
B. \(6.25(s + g)\)
C. \(13.50(s + g)\)
D. \(13.50s + g\)

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**Question 3 (5 points)**

Ken and Paul have been mowing lawns to earn extra money. Their jobs earn $65 per week. Ken worked for \(x\) weeks and earned an extra $18. Paul worked for \(y\) weeks. From the expressions below, select one that determines the total amount that Ken and Paul earned mowing lawns.

A. \(83x + 65y\)
B. \(65x − 18 + 65y\)
C. \(60x + 83y\)
D. \(65x + 18 + 65y\)

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**Question 4 (5 points)**

Michelle and her friends wondered who had the most pop albums in their music collection. She recorded the information below:

| Name | Number of Pop Albums | Total Number of Albums |
|----------|----------------------|------------------------|
| Michelle | 33 | 60 |
| Sasha | 36 | 78 |
| Kat | 40 | 89 |
| Monica | 24 | 59 |

Based on the survey, which friend had the greatest percentage of pop albums?

A. Michelle
B. Sasha
C. Kat
D. Monica

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**Question 5 (5 points)**

Lynne was wondering which game was more popular, so she asked her friends which they liked to play more, Fortnite or Among Us. She found that of the 80 people who responded, 0.55 of them preferred Fortnite, and 30% of them preferred Among Us. How many more of her friends prefer Fortnite than Among Us?

A. 30
B. 20
C. 44.45
D. 5

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**Question 6 (5 points)**

Hulk, Iron Man, Thor, and Captain America together clean out evil from 60 cities. Hulk cleaned up 0.25 of the cities, Iron Man cleaned up 12 of the 60 cities, Thor cleaned 35% of the cities, and Captain America cleaned up the remaining cities. Who cleaned up the most cities?

A. Hulk
B. Iron Man
C. Thor
D. Captain America

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**Question 7 (5 points)**

Solve for \(x\).

A. 12
B. \(-12\)
C. \(-35\)
D. 35

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**Question 8 (5 points)**

Clark Kent needs to buy some new glasses. He has $70 to spend and the glasses that he wants only cost $30. He wants to spend the remainder of his money on new capes. Each cape costs $8. Which inequality represents the number of capes he can purchase?

A. \(x \geq 5\)
B. \(x \leq 11\)
C. \(x \leq 5\)
D. \(x \geq 11\)

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**Question 9 (5 points)**

Find the equation that can represent the situation if the sum of two numbers is 32. We also know that the greater number is 5 more than the smaller number.

A. \(x + (x + 5) = 32\)
B. \(x - (x + 5) = 32\)
C. \(x(x + 5) = 32\)
D. \(x(x - 5) = 32\)

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**Question 10 (5 points)**

SpongeBob needs $44 to buy a new pair of rectangle pants. He has already been able to save $9 and plans to work as a cook where he can earn $7 per hour. Which inequality shows the minimum number of hours, \(n\), that SpongeBob will have to work as a cook to earn enough to buy the rectangle pants?

A. \(9 + 7n \leq 44\), so \(n \leq 5\)
B. \(9 + 7n \geq 44\), so \(n \geq 5\)
C. \(7n \geq 44 + 9\), so \(n \geq 7.8\)
D. \(7n \leq 44 + 9\), so \(n \leq 7.8\)

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**Question 11 (5 points)**

Jesse sells clothes in the Yee Haw! Western Clothing store and earns $40 per day. She earns an extra $5 for each lasso she sells. If Jesse wants to earn at least $70 per day, which inequality shows the minimum number of lassos, \(n\), that she would need to sell?

A. \(40 + 5n \leq 70\), so \(n \leq 6\)
B. \(40 + 5n \geq 70\), so \(n \geq 25\)
C. \(40 + 5n \leq 70\), so \(n \leq 25\)
D. \(40 + 5n \geq 70\), so \(n \geq 6\)

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**Question 12 (5 points)**

Defne was looking online and saw some cakes that looked delicious. Each cake costs $10.01 and has a shipping cost of $9.96 per order. If Defne wants to spend no more than $50 for the cakes, which inequality shows the maximum number of cakes, \(c\), Defne can buy?

A. \(9.96p - 10.01p \leq 50\), so \(p \leq 1\)
B. \(9.96p + 10.01p \leq 50\), so \(p \leq 2\)
C. \(9.96 - 10.01p \leq 50\), so \(p \leq 3\)
D. \(9.96 + 10.01p \leq 50\), so \(p \leq 4\)

Answer :

The correct answers are:

1. b

2. a

3. d

4. a

5. a

6. c

7. a

8. a

9. a

10. b

11. b

12. b

Let's analyze each question:

Question 1:

[tex]\[15a + 6\][/tex]

The equivalent expression is:[tex]\[3(5a + 2)\][/tex]

So, the correct answer is b. 3(5a + 2).

Question 2:

[tex]\[6.25s + g\][/tex]

This expression best represents the total money collected for attending the dance. Therefore, the correct answer is a. 6.25s + g.

Question 3:

[tex]\[65x + 18 + 65y\][/tex]

This expression determines the total amount that Ken and Paul earned mowing lawns. Therefore, the correct answer is d. 65x + 18 + 65y.

Question 4:

To find the friend with the greatest percentage of pop albums, calculate the percentage of pop albums for each friend:

a. Michelle: [tex]\(\frac{33}{60} \times 100 \approx 55\%\)[/tex]

b. Sasha: [tex]\(\frac{36}{78} \times 100 \approx 46.15\%\)[/tex]

c. Kat: [tex]\(\frac{40}{89} \times 100 \approx 44.94\%\)[/tex]

d. Monica: [tex]\(\frac{24}{59} \times 100 \approx 40.68\%\)[/tex]

So, the correct answer is a. Michelle.

Question 5:

Calculate the difference in preference:

[tex]\[0.55 - 0.30 = 0.25\][/tex]

So, the correct answer is a. 30.

Question 6:

Calculate the number of cities each cleaned:

a. Hulk:[tex]\(0.25 \times 60 = 15\)[/tex]

b. Iron Man: [tex]\(12\)[/tex]

c. Thor:[tex]\(0.35 \times 60 = 21\)[/tex]

d. Captain America: [tex]\(60 - 15 - 12 - 21 = 12\)[/tex]

So, the correct answer is c. Thor.

Question 7:

Solve for [tex]\(x\) in \(2x - 7 = 17\):[/tex]

[tex]\[2x = 24\][/tex]

[tex]\[x = 12\][/tex]

So, the correct answer is a. 12.

Question 8:

Write the inequality for the number of capes [tex](\(x\)):[/tex]

[tex]\[x = \frac{70 - 30}{8}\][/tex]

[tex]\[x = \frac{40}{8}\][/tex]

[tex]\[x = 5\][/tex]

So, the correct answer is a. [tex]\(x \geq 5\)[/tex]

Question 9:

The correct equation is a. [tex]\(x + (x + 5) = 32\)[/tex]

Question 10:

The correct inequality is b. [tex]\(9 + 7n \geq 44\), so \(n \geq 5\)[/tex]

Question 11:

The correct inequality is b. [tex]\(40 + 5n \geq 70\), so \(n \geq 6\)\\[/tex]

Question 12:

The correct inequality is [tex]b. \(9.96p + 10.01p \leq 50\), so \(p \leq 2\).[/tex]

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