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

Question

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 1

To find the correct equation, let's break down the information given in the problem.

Lee scored 25 points, and this score is described as "3 more than twice the number of points Alex scored." We can express this relationship mathematically.

Let \( a \) be the number of points Alex scored. According to the problem, two times Alex's score plus 3 equals Lee's score:

\[ 2a + 3 = 25 \]

We can rearrange this equation to match one of the options provided. Subtracting 3 from both sides gives:

\[ 2a = 25 - 3 \] \[ 2a = 22 \]

Now we can identify which option matches:

The equation that matches our derived equation is:

\[ 25 = 3 + 2a \]

Thus, the answer is:

B. 25 = 3 + 2a

Answer 2

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 3

To find out how many apples Ellen can buy next week, we first need to determine the cost per apple based on her purchases from last week and this week.

Last week:

• Cost: $2.40 for 4 apples
• Cost per apple: \[ \frac{2.40}{4} = 0.60 \text{ (or 60 cents)} \]

This week:

• Cost: $5.40 for 9 apples
• Cost per apple: \[ \frac{5.40}{9} = 0.60 \text{ (or 60 cents)} \]

Since we found that the cost per apple remains at $0.60, we can use this value to analyze the options provided.

Now, let's evaluate each option:

A. 1 apple for $1.20

• Cost per apple: $1.20 (not correct, as it should be $0.60)

B. 6 apples for $3.40

• Cost per apple: \[ \frac{3.40}{6} \approx 0.5667 \text{ (not $0.60, so not correct)} \]

C. 10 apples for $6.00

• Cost per apple: \[ \frac{6.00}{10} = 0.60 \text{ (this works)} \]

D. 13 apples for $8.20

• Cost per apple: \[ \frac{8.20}{13} \approx 0.6308 \text{ (not $0.60, so not correct)} \]

The only option that maintains the cost per apple at $0.60 is:

C. 10 apples for $6.00

Thus, Ellen could buy 10 apples for $6.00 next week.

Answer 4

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 5

To find the unit rate for brake pads produced per hour, we can analyze the data provided in the problem.

From the table, we know the following:

• 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.

To find the rate of production in brake pads per hour, we can use the total number of brake pads produced in the 12-hour period:

\[ \text{Total brake pads produced in 12 hours} = 192 \]

Now, we calculate the unit rate:

\[ \text{Unit rate} = \frac{\text{Total brake pads produced}}{\text{Total hours}} = \frac{192 \text{ brake pads}}{12 \text{ hours}} = 16 \text{ brake pads per hour} \]

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

D. 16 brake pads per hour