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

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.