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 went 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

5 answers

Let's break down the earnings for Amy and Ben:

  1. Amy's Earnings: Amy's total earnings for the week can be calculated as: \[ \text{Amy's Earnings} = 12 \times a \]

  2. Ben's Earnings: Ben's total earnings will include his regular pay plus his overtime pay. His regular pay is calculated as: \[ \text{Ben's Regular Earnings} = 12 \times b \] Adding his overtime pay of $46: \[ \text{Ben's Total Earnings} = 12 \times b + 46 \]

Now, to find the total amount of money they will make this week: \[ \text{Total Earnings} = \text{Amy's Earnings} + \text{Ben's Total Earnings} \] \[ \text{Total Earnings} = (12 \times a) + (12 \times b + 46) \] \[ \text{Total Earnings} = 12a + 12b + 46 \]

Based on this breakdown, here are some possible true statements you might find related to their earnings:

  1. Amy earns $12 per hour for each hour she works.

    • This is true.
  2. Ben earns $12 per hour for each hour he works plus an additional $46 from overtime.

    • This is also true.
  3. The total amount they earn together can be expressed as \(12(a + b) + 46\).

    • This is true as well, as it simplifies from \(12a + 12b + 46\).
  4. If Amy works more hours than Ben, she will make more than Ben.

    • This statement is not always true because Ben's overtime pay can significantly increase his total earnings.

Therefore, the two statements that are true would be:

  • Amy earns $12 per hour for each hour she works.
  • Ben earns $12 per hour for each hour he works plus an additional $46 from overtime.

If you have specific statements provided, please share them for more tailored answers!

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

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

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

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

Let's evaluate each of the provided statements regarding the expressions to determine which are true:

  1. 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 for the total earnings is \(12a + 12b + 46\) (i.e., 12 times Amy's hours plus 12 times Ben's hours plus Ben's overtime). The expression \(12(a + b) + 46\) incorrectly combines the total hours worked without considering the hourly wage for each person's individual hours.
  2. The expression \(12a + 58b\) shows the sum of the amount of money Amy made and the amount of money Ben made.

    • False. The earnings for Ben would need to account for his overtime pay, so the correct expression should be \(12a + (12b + 46)\) or \(12a + 12b + 46\) rather than \(12a + 58b\).
  3. 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 expression does not accurately represent their earnings. The components of hourly earnings and overtime pay are misused, and it does not provide the correct representation of their total earnings.
  4. The expression \(12a + (12b + 46)\) shows the sum of the amount of money Amy made and the amount of money Ben made.

    • True. This expression correctly represents the earnings where \(12a\) is the amount Amy makes, \(12b\) is the amount Ben makes, and \(46\) is added for Ben's overtime pay.

Therefore, the only true statement is the fourth one:

  • The expression \(12a + (12b + 46)\) shows the sum of the amount of money Amy made and the amount of money Ben made.
but I need two

Let's reassess the statements and find the two that can be deemed as true:

  1. 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. This expression does not correctly represent their combined earnings.
  2. The expression \(12a + 58b\) shows the sum of the amount of money Amy made and the amount of money Ben made.

    • False. This expression is incorrect because it does not account for Ben's overtime pay accurately.
  3. 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 expression is also incorrect in its representation of their earnings.
  4. 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 expresses Amy’s pay and Ben’s pay, including the overtime.

Conclusion

To fulfill your requirement of identifying two true statements, I apologize for the earlier oversight. It seems one expression correctly states their total earnings. Let's note that from the provided options, only one expression is true.

If you must identify two statements from any context or additional information, please clarify, or if you have any other examples, please share, and I would be happy to analyze them!