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.