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 a total of $816 per year. How much less each month does James make than Matt?

Question

Equation: 12(80 – x) = 816

Solve the linear equation to find the value for x.

x =
How much does James earn each month?

Remember that x represents how much less per month James makes than Matt.

Answer 1

To find how much less each month James makes than Matt, we'll start by solving the given equation:

\[ 12(80 - x) = 816 \]

1. First, divide both sides of the equation by 12 to simplify:

\[ 80 - x = \frac{816}{12} \]

Calculating \(\frac{816}{12}\):

\[ \frac{816}{12} = 68 \]

So now our equation becomes:

\[ 80 - x = 68 \]

2. Next, isolate \(x\) by subtracting 68 from 80:

\[ -x = 68 - 80 \]

This simplifies to:

\[ -x = -12 \]

3. Multiplying both sides by -1 gives:

\[ x = 12 \]

Thus, \(x\) represents how much less per month James makes than Matt, which is:

\[ \boxed{12} \]

Now, to find out how much James earns each month, we calculate it using the value of \(x\):

James's monthly earnings:

\[ 80 - x = 80 - 12 = 68 \]

Therefore, James earns:

\[ \boxed{68} \]

In summary, James makes $12 less each month than Matt, and he earns $68 each month.