Question

James earned $816 each year. He earned x dollars less per month than Matt, who earned $80 per month.

Equation: 12(80 – x) = 816

    x = 12; monthly earnings = $68

Which strategies will verify that the value for x is correct? Check all that apply.
Substitute 68 for x in the equation.
Substitute 12 for x in the equation.
Multiply $68 by 12 months.
Multiply $80 by 12 months.

Answer 1

To verify that the value for \( x \) is correct, you can use the following strategies:

1. **Substitute 12 for x in the equation.**
- If you replace \( x \) with 12 in the equation \( 12(80 - x) = 816 \), you can check if the equation holds true.
- \( 12(80 - 12) = 12(68) = 816 \), which confirms that \( x = 12 \) is correct.

2. **Multiply $68 by 12 months.**
- Since you derived that Matt's earnings per month are $68 (which is $80 - $12), if you multiply $68 by 12, you should also arrive at $816.
- \( 68 \times 12 = 816 \), confirming that the income is accurate.

The other two strategies would not verify whether \( x \) is correct:

- **Substitute 68 for x in the equation.**
- This step is inappropriate because \( x \) represents how much less Matt earns compared to James, and using $68 here doesn't apply directly as \( x \).

- **Multiply $80 by 12 months.**
- While this would calculate Matt's total earned amount of $960, it doesn't directly help to verify whether \( x \) is correct in the context of James' earnings.

Therefore, the two valid strategies to verify that the value for \( x \) is correct are:

- Substitute 12 for \( x \) in the equation.
- Multiply $68 by 12 months.