Question

For the mowing that Sandy is going to do, she purchased a weed eater for $150 and figures she will need to buy a new spool of weed-eating string for each yard, which costs $10 a spool. How many yards will she need to mow to break even if she's still charging $20 per yard?

Answer 1

To determine how many yards Sandy needs to mow to break even, we need to account for her initial costs and her variable costs for each yard mowed.

1. **Initial costs:**
- Cost of the weed eater: $150

2. **Variable costs per yard:**
- Cost of the weed-eating string: $10 per yard

3. **Revenue per yard:**
- Charge per yard: $20

4. **Calculating total costs and revenues:**
- Total costs for mowing \( x \) yards can be expressed as:
\[
\text{Total Costs} = \text{Initial Cost} + (\text{Variable Cost per Yard} \times \text{Number of Yards})
\]
\[
\text{Total Costs} = 150 + 10x
\]

- Total revenue for mowing \( x \) yards can be expressed as:
\[
\text{Total Revenue} = \text{Charge per Yard} \times \text{Number of Yards}
\]
\[
\text{Total Revenue} = 20x
\]

5. **Finding the break-even point:**
To find the break-even point, set the total costs equal to the total revenue:
\[
150 + 10x = 20x
\]

6. **Solving for \( x \):**
Rearranging the equation:
\[
150 = 20x - 10x
\]
\[
150 = 10x
\]
\[
x = \frac{150}{10} = 15
\]

Thus, Sandy needs to mow **15 yards** to break even.