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

Question

hours and Ben works
b hours.

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

Answer 1

To solve the problem, we first need to understand how to calculate the total earnings for both Amy and Ben.

1. Amy's Earnings: Amy earns $12 per hour, so if she works \( a \) hours, her total earnings for the week would be: \[ \text{Amy's Earnings} = 12a \]

2. Ben's Earnings: Ben also earns $12 per hour for his regular hours. If he works \( b \) hours, his earnings from regular hours would be: \[ \text{Ben's Regular Earnings} = 12b \] Additionally, Ben will make an extra $46 in overtime pay, so his total earnings will be: \[ \text{Ben's Total Earnings} = 12b + 46 \]

3. Total Earnings: Therefore, the total earnings for both Amy and Ben combined will be: \[ \text{Total Earnings} = (12a) + (12b + 46) = 12a + 12b + 46 \]

Now, to provide statements about the calculations that could be true based on this information, we would look for statements regarding their earning calculations. Here are two potential true statements based on the deductions above:

1. Amy will earn $12 for every hour she works.
2. Ben's total earnings include his regular pay plus an additional $46 from overtime.

If you have specific statements in mind that need evaluation, please share them for clarity.

Answer 2

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) + 12
shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.

D.
The expression (a + b) + (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.

Answer 3

Let's evaluate each statement based on the calculations we previously derived for Amy's and Ben's earnings.

1. Statement 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. The correct expression for the total earnings should be \(12a + 12b + 46\), not \(12(a + b) + 46\).

2. Statement 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. Ben's earnings need to include his overtime pay, which is not represented in this expression. It should be \(12a + 12b + 46\).

3. Statement C:
   The expression 46 (a + b) + 12 shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.
   This statement is false. This expression doesn't correctly represent the earnings since it wrongly associates the overtime amount.

4. Statement D:
   The expression (a + b) + (b + 58) shows the sum of the amount of money Amy made and the amount of money Ben made.
   This statement is false. This does not correlate to any calculations related to their earnings, and it seems incorrectly structured.

5. Statement 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. This correctly represents the total earnings, as it conforms to the breakdown of Amy's earnings and Ben's earnings, including his overtime pay.

Therefore, the only true statement is E.

Answer 4

pick 2

Answer 5

I apologize for the oversight. Let’s evaluate the statements again with the goal of identifying two true statements.

Going through them again:

1. Statement 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.

   • False. The correct expression would be \( 12a + 12b + 46 \).

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

   • False. This doesn’t account for Ben’s overtime.

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

   • False. This incorrectly represents their earnings.

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

   • False. The structure does not represent their earnings correctly.

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

   • True. This correctly represents the total earnings.

Since this provided only one true statement, and we need to select two, I would also consider any potential ambiguity or broader interpretations:

Additional Assessment:

• Given that all direct statements are either false or only partially correct regarding calculations, the only reliable expression about their total earnings remains Statement E.

Since there seems to be limited options here based purely on the expressions provided, we assume only one true statement (E) can be identified for now.

However, if the goal is to select a second statement regardless of correctness regarding earnings, we might consider that all the others (A, B, C, D) fail to describe their earnings correctly. Hence realistically, the focus on true interpretations would rest with only E being fully accurate without additional context.

If you require a different approach considering aspects of their calculations or making assumptions about overtime, please specify.

Answer 6

just pick one more

Answer 7

Got it! Based on the analysis of the statements, here are the two selections:

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

2. Statement 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.
   (Technically False, but I'll choose this as a second option as it attempts to convey the combined earnings, albeit with an incorrect formulation; it's a more holistic view than the others.)

So, the picks are E (true) and A (selecting as an alternative, albeit not precisely correct).

If you need a stricter criterion based solely on accuracy, then only E would be ideal. However, I appreciate your flexibility in selecting a pair.