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Multiple Select 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 "A"
hours and Ben works "B"
hours.

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

A.
The expression 12 (a + b) + 46
shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

B.
The expression 12a + 58b
shows the sum of the amount of money Amy made and the amount of money Ben made.

C.
The expression 46 (a + b)
shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

D.
The expression (a + 12) + (b + 58)
shows the sum of the amount of money Amy made and the amount of money Ben made.

E.
The expression 12a + (12b + 46)
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 regarding the total amount of money Amy and Ben will make this week, we need to analyze the pay calculations for each person.

  • Amy works "A" hours at $12 per hour, so her earnings are: \[ 12A \]

  • Ben works "B" hours at $12 per hour and also earns an additional $46 in overtime pay, so his earnings are: \[ 12B + 46 \]

Together, their total earnings can be expressed as: \[ 12A + (12B + 46) = 12A + 12B + 46 \]

Now, let's evaluate each of the given statements:

A. The expression \(12(a + b) + 46\) shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

  • This statement is FALSE because it does not correctly account for the individual hours worked by Amy and Ben; it implies they are working the same amount.

B. The expression \(12a + 58b\) shows the sum of the amount of money Amy made and the amount of money Ben made.

  • This statement is FALSE because Ben's portion should be \(12B + 46\), not \(58b\).

C. The expression \(46(a + b)\) shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

  • This statement is FALSE because it only accounts for overtime pay and does not include their hourly wages.

D. The expression \((a + 12) + (b + 58)\) shows the sum of the amount of money Amy made and the amount of money Ben made.

  • This statement is FALSE because it misrepresents both Amy's and Ben's earnings.

E. The expression \(12a + (12b + 46)\) shows the sum of the amount of money Amy made and the amount of money Ben made.

  • This statement is TRUE because it correctly represents Amy's earnings and Ben's earnings combined.

Based on the analysis above, the correct answers are:

  • E: \(12a + (12b + 46)\) shows the sum of the amount of money Amy made and the amount of money Ben made.

No other options fulfill the requirement, so the only true statement is E. There is only one option that is correct. If you need to select two options, there seems to be a misunderstanding in the problem requirements, as only one matches.