Question

During the summer, Jody earns $9 per hour babysitting and $10 per hour doing yard work. This week she worked 34 hours and earned $410. If x represents the number of hours she babysat and y represents the number of hours she did yard work, which system of equations models this situation?

Answer 1

To model the situation with a system of equations, we need to consider the information provided:

1. Jody earns $9 per hour babysitting and $10 per hour doing yard work.
2. She worked a total of 34 hours.
3. She earned a total of $410.

Let:
- \( x \) = number of hours babysitting
- \( y \) = number of hours doing yard work

From the information given, we can set up the following two equations:

1. The total hours worked equation:
\[
x + y = 34
\]

2. The total earnings equation:
\[
9x + 10y = 410
\]

Thus, the system of equations that models this situation is:

\[
\begin{cases}
x + y = 34 \\
9x + 10y = 410
\end{cases}
\]