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
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.
hours and Ben works b
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.
Answers
GPT-4o mini
To assess which of the statements are true, let's first determine how to represent the earnings of Amy and Ben mathematically.
1. **Amy's Earnings:**
- Amy works \( a \) hours at $12 per hour, so her earnings would be:
\[
12a
\]
2. **Ben's Earnings:**
- Ben works \( b \) hours at $12 per hour, so for his regular hours, he earns:
\[
12b
\]
- Additionally, Ben makes $46 in overtime pay.
So, Ben’s total earnings this week can be expressed as:
\[
12b + 46
\]
3. **Combined Earnings of Amy and Ben:**
- To find the total earnings for both, we combine their earnings:
\[
12a + (12b + 46) = 12a + 12b + 46
\]
Now let’s analyze the statements provided in relation to this calculation:
**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** because \( 12a + 12b + 46 \) indeed represents the total earnings combining hourly pay and overtime.
**B.** The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- While this is somewhat ambiguous, if we assume "the expression" refers specifically to \( 12a + 12b \) without overtime, then it would be false. However, if "the expression" includes the total \( 12a + 12b + 46 \), it is true.
**C.** The expression shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.
- This statement is **true** because it similarly reflects the total earnings, including both regular and overtime pay.
**D.** The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- This is **true** as it reflects the correct total summation of their earnings.
**E.** The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- This is potentially a repetition or misleading without context, but assuming it refers to the summed total including overtime, it could also be interpreted as true.
Therefore, the two statements that are definitively true, based on the formulated expressions:
- **A.** (combined earnings including overtime)
- **C.** (combined earnings including overtime)
Thus, the correct answers are A and C.
1. **Amy's Earnings:**
- Amy works \( a \) hours at $12 per hour, so her earnings would be:
\[
12a
\]
2. **Ben's Earnings:**
- Ben works \( b \) hours at $12 per hour, so for his regular hours, he earns:
\[
12b
\]
- Additionally, Ben makes $46 in overtime pay.
So, Ben’s total earnings this week can be expressed as:
\[
12b + 46
\]
3. **Combined Earnings of Amy and Ben:**
- To find the total earnings for both, we combine their earnings:
\[
12a + (12b + 46) = 12a + 12b + 46
\]
Now let’s analyze the statements provided in relation to this calculation:
**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** because \( 12a + 12b + 46 \) indeed represents the total earnings combining hourly pay and overtime.
**B.** The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- While this is somewhat ambiguous, if we assume "the expression" refers specifically to \( 12a + 12b \) without overtime, then it would be false. However, if "the expression" includes the total \( 12a + 12b + 46 \), it is true.
**C.** The expression shows the combined amount of money Amy and Ben made for their hourly work plus the overtime amount.
- This statement is **true** because it similarly reflects the total earnings, including both regular and overtime pay.
**D.** The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- This is **true** as it reflects the correct total summation of their earnings.
**E.** The expression shows the sum of the amount of money Amy made and the amount of money Ben made.
- This is potentially a repetition or misleading without context, but assuming it refers to the summed total including overtime, it could also be interpreted as true.
Therefore, the two statements that are definitively true, based on the formulated expressions:
- **A.** (combined earnings including overtime)
- **C.** (combined earnings including overtime)
Thus, the correct answers are A and C.