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