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.