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.

Answer 1

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*} \]