Multiple Choice Question

Question

Jackson is given the expression below to simplify.

9x – 4 + 4x + 5x + 19

Which expression is equivalent to Jackson's expression?

A.
3(6x + 5)

B.
18x + 23

C.
5(x + 2)

D.
14x + 19

Answer 1

To simplify the expression \(9x - 4 + 4x + 5x + 19\), we first combine the like terms.

1. Combine the coefficients of \(x\): \[ 9x + 4x + 5x = 18x \]

2. Combine the constant terms: \[ -4 + 19 = 15 \]

Now, put the simplified terms together: \[ 18x + 15 \]

Let's compare \(18x + 15\) with the answer choices given:

A. \(3(6x + 5)\) simplifies to \(18x + 15\) (this is equivalent).

B. \(18x + 23\) does not match.

C. \(5(x + 2)\) simplifies to \(5x + 10\) (this does not match).

D. \(14x + 19\) does not match.

The correct answer is:

A. \(3(6x + 5)\).

Answer 2

Multiple Choice Question
Lee scored 25 points in yesterday's game. That was 3 more than twice the number of points Alex scored.

Which equation can be used to find, a, the number of points Alex scored?
A.
25 + 3 = 2a

B.
25 = 3 + 2a

C.
2(25) + 3 = a

D.
2(25) = 3 + a

Answer 3

To find the equation that represents the information given in the problem, we can break it down step by step.

Lee scored 25 points, which is described as "3 more than twice the number of points Alex scored". We can represent Alex's score with the variable \( a \).

The statement "3 more than twice the number of points Alex scored" can be written in equation form as: \[ 2a + 3 \]

This means that: \[ 25 = 2a + 3 \]

Now we can rearrange this into a standard form if needed: \[ 25 - 3 = 2a \quad \text{or} \quad 25 = 2a + 3 \]

Looking at the answer choices:

A. \(25 + 3 = 2a\) (Incorrect)

B. \(25 = 3 + 2a\) (This is correct!)

C. \(2(25) + 3 = a\) (Incorrect)

D. \(2(25) = 3 + a\) (Incorrect)

Thus, the correct equation to find \( a \), the number of points Alex scored, is:

B. \(25 = 3 + 2a\).

Answer 4

Multiple Choice Question
Last week, Ellen bought 4 apples for $2.40. This week she bought 9 apples for $5.40. If the cost per apple remains the same, how many apples could she buy next week?
A.
1 apple for $1.20

B.
6 apples for $3.40

C.
10 apples for $6.00

D.
13 apples for $8.20

Answer 5

To determine how many apples Ellen could buy next week, we first need to find the cost per apple based on her purchases.

Step 1: Calculate the cost per apple

Last week:

• Ellen bought 4 apples for $2.40.
• Cost per apple = Total Cost / Number of Apples = \( \frac{2.40}{4} = 0.60 \) dollars per apple.

This week:

• Ellen bought 9 apples for $5.40.
• Cost per apple = \( \frac{5.40}{9} = 0.60 \) dollars per apple.

Step 2: Determine how many apples she could buy next week at the same price

Assuming she has a certain budget, we can test each option to see how many apples she could buy based on the $0.60 per apple price.

1. A. 1 apple for $1.20

   • Cost = $1.20 (not correct since it's more than $0.60 per apple).

2. B. 6 apples for $3.40

   • Cost = \( 6 \times 0.60 = 3.60 \) (not correct since it's under the price).

3. C. 10 apples for $6.00

   • Cost = \( 10 \times 0.60 = 6.00 \) (this is correct).

4. D. 13 apples for $8.20

   • Cost = \( 13 \times 0.60 = 7.80 \) (not correct).

Conclusion

Based on her cost per apple of $0.60, the only option that matches the cost calculation correctly is:

C. 10 apples for $6.00.

Answer 6

Multiple Choice Question
The table below shows the total number of brake pads produced by machines throughout a 12-hour work day.

The table shows the number of brake pads produced in 3 hours is 48, 6 hours is 96, 9 hours is 144, and 12 hours is 192.

What is the unit rate for brake pads produced per hour?

A.
4 brake pads per hour

B.
3 brake pads per hour

C.
12 brake pads per hour

D.
16 brake pads per hour

Answer 7

To determine the unit rate for brake pads produced per hour, we can look at the total number of brake pads produced in a specified time frame and calculate the rate.

From the data provided in the table:

• In 3 hours, 48 brake pads are produced.
• In 6 hours, 96 brake pads are produced.
• In 9 hours, 144 brake pads are produced.
• In 12 hours, 192 brake pads are produced.

Let's find the unit rate using the 12-hour data, which is the easiest as it gives a complete production in one full workday.

Calculation of unit rate:

In 12 hours, 192 brake pads are produced.

To find the unit rate (brake pads per hour): \[ \text{Unit Rate} = \frac{\text{Total Brake Pads Produced}}{\text{Total Hours}} = \frac{192 \text{ brake pads}}{12 \text{ hours}} = 16 \text{ brake pads per hour} \]

Thus, the unit rate for brake pads produced per hour is:

D. 16 brake pads per hour.

Answer 8

Multiple Choice Question
Eric is baking a cake. The recipe calls for
2 1/2
pounds of flour for every
1/4
cup of sugar. How many pounds of flour should Eric use for 1
cup of sugar?

A.
1/10

B.
5/8

C.
4
D.

10

Answer 9

To determine how many pounds of flour Eric should use for 1 cup of sugar, we start by looking at the ratio given in the recipe.

The recipe states that for every \( \frac{1}{4} \) cup of sugar, Eric should use \( 2 \frac{1}{2} \) pounds of flour.

Step 1: Convert \( 2 \frac{1}{2} \) to an improper fraction

\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2} \text{ pounds of flour} \]

Step 2: Set up a proportion to find the amount of flour for 1 cup of sugar

Since \( \frac{1}{4} \) cup of sugar corresponds to \( \frac{5}{2} \) pounds of flour, we can express the relationship as follows:

If \( \frac{1}{4} \) cup of sugar requires \( \frac{5}{2} \) pounds of flour, then 1 cup of sugar (which is 4 times \( \frac{1}{4} \) cup) will require:

\[ 4 \times \frac{5}{2} = \frac{20}{2} = 10 \text{ pounds of flour} \]

Conclusion

Thus, Eric should use:

D. 10 pounds of flour.

Answer 10

Multiple Choice Question
Mr. Reynolds goes for a morning walk. The graph below shows the relationship between how many minutes he has walked, x, and the distance in feet he has walked, y.

The graph has numbers from 0 to 20 in increments of 4 on the x-axis and from 0 to 5,000 in increments of 500 on the y-axis. A straight line starts from (0, 0) and passes through (4, 1,000), (8, 2,000), (12, 3,000), (16, 4,000), and (20, 5,000).

What is the meaning of the point
on the graph?

A.
It means that Mr. Reynolds walks 8 miles in 2,000 minutes.

B.
It means that Mr. Reynolds walks 2,000 feet in 8 minutes.

C.
It means that Mr. Reynolds walks 2,000 feet per minute for 8 minutes.

D.
It means that Mr. Reynolds walks 8 feet in 2,000 minutes.

Answer 11

To interpret the point on the graph, let's analyze the axes given in the problem:

• The x-axis represents the number of minutes Mr. Reynolds has walked, which ranges from 0 to 20 minutes.
• The y-axis represents the distance in feet walked, ranging from 0 to 5,000 feet.

The specific point you mentioned on the graph is \( (8, 2,000) \), where:

• \( 8 \) is the number of minutes walked (x-value).
• \( 2,000 \) is the distance in feet walked (y-value).

Interpretation of the Point (8, 2,000)

This point indicates that after walking for 8 minutes, Mr. Reynolds has covered a distance of 2,000 feet.

Now, reviewing the provided answer choices:

A. It means that Mr. Reynolds walks 8 miles in 2,000 minutes. (Incorrect, as the units and values don't match)

B. It means that Mr. Reynolds walks 2,000 feet in 8 minutes. (Correct, this matches the point on the graph)

C. It means that Mr. Reynolds walks 2,000 feet per minute for 8 minutes. (Incorrect, as it misinterprets the data, it isn't per minute)

D. It means that Mr. Reynolds walks 8 feet in 2,000 minutes. (Incorrect, as it does not match the values on the graph)

Conclusion

The correct interpretation of the point \( (8, 2,000) \) on the graph is:

B. It means that Mr. Reynolds walks 2,000 feet in 8 minutes.