Question

Matt makes $80 a month mowing lawns. His friend James also mows lawns, but he makes x dollars less per month than Matt does. James makes $816 per year. How much less each month does James make than Matt?

Which expression represents the amount of money James makes each month?


Which equation represents the scenario?

Answer 1

To solve the problem, we need to determine how much James makes each month and how that compares to Matt's monthly income.

1. **Monthly Income for Matt**:
- Matt makes $80 a month.

2. **James's Monthly Income**:
- James makes $816 per year. To find his monthly income, we divide by the number of months in a year:
\[
\text{James's monthly income} = \frac{816}{12} = 68 \text{ dollars}
\]

3. **Amount James makes less than Matt**:
- Since Matt makes $80 a month, we can find out how much less James makes by subtracting James's monthly income from Matt's:
\[
80 - 68 = 12 \text{ dollars}
\]

### Expressions and Equations

**1. Expression representing the amount of money James makes each month**:
The expression for James's monthly income can be written as:
\[
\text{James's monthly income} = 68
\]

**2. Equation representing the scenario**:
Since we know that James makes \( x \) dollars less per month than Matt, we can express this using an equation:
\[
80 - x = 68
\]
Here, \( x \) represents the amount of money James makes less than Matt each month.

By solving this equation, you can confirm that \( x = 12 \), which tells us that James makes $12 less than Matt each month.