Question

Amy and Ben each get paid an hourly wage of $12 per hour. This week, Ben will make an additional $46 in overtime pay. They want to calculate the total amount of money they will make this week if Amy works
hours and Ben works
hours.

Which of the following statements are true? Select two that apply.

A.
The expression
shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

B.
The expression
shows the sum of the amount of money Amy made and the amount of money Ben made.

C.
The expression
shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

D.
The expression
shows the sum of the amount of money Amy made and the amount of money Ben made.

E.
The expression
shows the sum of the amount of money Amy made and the amount of money Ben made.

Answer 1

To determine which statements are true, we need to understand how to calculate Amy and Ben's total earnings for the week.

Let:
- **A** be the number of hours Amy works.
- **B** be the number of hours Ben works.

Each earns $12 per hour, and Ben also earns an additional $46 in overtime.

The total pay for each of them can be represented as follows:
- Amy's total pay: \( 12A \)
- Ben's total pay including overtime: \( 12B + 46 \)

Thus, the combined total amount of money they make this week would be:

\[
Total = 12A + (12B + 46) = 12A + 12B + 46
\]

Now, let's evaluate the statements:

A. The expression shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.
- This statement aligns with our total calculation. It is **True**.

B. The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- Since Ben's overtime is included in his total, this statement is **False** without specifying overtime.

C. The expression shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.
- This is similar to statement A and is **True**.

D. The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- Like statement B, this is **False** unless it specifies that Ben's total includes overtime.

E. The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- This is also **False** unless overtime is specified.

Thus, the two true statements are:
- **A**: The expression shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.
- **C**: The expression shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

So, the correct answers are **A** and **C**.