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?

Question

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.