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

Question

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 the total earnings for Amy and Ben based on their hourly work and Ben's overtime pay.

1. Hourly Earnings Calculation:

   • Amy's total earnings = Hourly Wage × Hours Worked = \(12 \cdot \text{(hours worked by Amy)}\)
   • Ben's total earnings = Hourly Wage × Hours Worked + Overtime Pay = \(12 \cdot \text{(hours worked by Ben)} + 46\)

2. Combined Earnings:

   • Total combined earnings = Amy's total earnings + Ben's total earnings
   • This can be expressed as: \( (12 \cdot \text{(hours worked by Amy)}) + (12 \cdot \text{(hours worked by Ben)} + 46) \)

With this understanding, let's analyze the possible truths of the given statements:

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

• This statement is true if the expression includes both Amy and Ben's earnings from hourly work and also includes Ben's overtime pay.

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

• This statement is true if the expression indicates Amy's earnings and Ben's earnings without reference to overtime.

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

• This statement is similar to A and is true if the expression includes hourly wages for both plus overtime.

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

• This statement is true if it indicates that the total includes Amy's earnings plus Ben's basic earnings without overtime.

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

• This statement is functionally similar to D, and it would also be true based on the same understanding.

Given this breakdown, the two most fitting true statements would be:

• C: It encompasses both the hourly wages and overtime.
• D: It reflects the sum of Amy’s and Ben’s earnings correctly.

Thus, the best answers to select are C and D.