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.

1 answer

To determine which statements are true, let's analyze the earning expressions based on the information provided.

Assuming:

  • Amy works \( x \) hours.
  • Ben works \( y \) hours.

Their respective wages are:

  • Amy's earnings: \( 12x \) (since she makes $12 per hour)
  • Ben's earnings (including overtime): \( 12y + 46 \) (regular pay plus overtime)

Now, let's write out the two possible expressions for their total earnings:

  1. The total amount they will make this week can be expressed as: \[ \text{Total Earnings} = 12x + (12y + 46) = 12x + 12y + 46 \] This means:
    • The part \( 12x + 12y \) represents their combined earnings from their hourly work, and the \( +46 \) represents the additional overtime pay Ben receives.

Based on this setup, the statements can be evaluated:

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.

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

  • This statement can also be seen as true because it refers to the total amount without breaking it into separate components.

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

  • This statement repeats the structure of A and is true as explained above.

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

  • This statement is also true, as it describes the total earnings validly.

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

  • This statement is again similar to D and is true.

Since we only need to select two statements that apply, the selections can be:

  • A and C (or alternatively B and D, as they are also valid).

Please confirm which expressions have specific components if available, to finalize the selection more precisely.