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. How many yards did she mow and how many yards did she rake leaves

Answer 1

To find how many yards Sandy mowed (m) and how many yards she raked leaves (r), we can set up a system of equations based on the information given:

1. \( r + m = 14 \) (Equation 1: the total number of yards)
2. \( 10r + 20m = 200 \) (Equation 2: the total profit)

Now, let's solve these equations step by step.

From Equation 1, we can express r in terms of m:

\[
r = 14 - m
\]

Now, we can substitute this expression for r into Equation 2:

\[
10(14 - m) + 20m = 200
\]

Expanding this gives us:

\[
140 - 10m + 20m = 200
\]

Combining like terms results in:

\[
140 + 10m = 200
\]

Now, we isolate m:

\[
10m = 200 - 140
\]
\[
10m = 60
\]
\[
m = 6
\]

Now that we have the value of m (the number of lawns mowed), we can substitute m back into Equation 1 to find r:

\[
r + 6 = 14
\]
\[
r = 14 - 6
\]
\[
r = 8
\]

Thus, Sandy raked leaves on 8 yards and mowed 6 lawns.

So the final answer is:
- Yards mowed (m): **6**
- Yards raked (r): **8**