Question
Sandy did yard work to raise money for her local animal shelter. Sandy raked leaves, r, at a profit of $10 per yard and mowed lawns, m, at $20 each. She worked on 14 different yards and made a profit of $200. Write a pair of linear equations that model this situation.
Answers
GPT-4o mini
To model the situation described, we can create two linear equations based on the information provided about Sandy's work.
1. **Number of yards equation:** Sandy raked leaves and mowed lawns on a total of 14 yards. We can express this as:
\[
r + m = 14
\]
where \( r \) is the number of yards she raked leaves, and \( m \) is the number of yards she mowed.
2. **Profit equation:** For her profits, she made $10 for each yard raked and $20 for each yard mowed. The total profit from both activities is $200, which can be expressed as:
\[
10r + 20m = 200
\]
So, the pair of linear equations that model this situation is:
\[
\begin{align*}
1) & \quad r + m = 14 \\
2) & \quad 10r + 20m = 200
\end{align*}
\]
1. **Number of yards equation:** Sandy raked leaves and mowed lawns on a total of 14 yards. We can express this as:
\[
r + m = 14
\]
where \( r \) is the number of yards she raked leaves, and \( m \) is the number of yards she mowed.
2. **Profit equation:** For her profits, she made $10 for each yard raked and $20 for each yard mowed. The total profit from both activities is $200, which can be expressed as:
\[
10r + 20m = 200
\]
So, the pair of linear equations that model this situation is:
\[
\begin{align*}
1) & \quad r + m = 14 \\
2) & \quad 10r + 20m = 200
\end{align*}
\]