Question

Ron is planning to sell handmade aprons for $25 each. So far, he spent $85 on a sewing machine and $32 on other sewing tools. The fabric for each apron will cost him $16.
How many aprons must Ron sell for his sales to equal his expenses?
aprons

Answer 1

To determine how many aprons Ron must sell for his sales to equal his expenses, we need to first calculate his total fixed costs and his variable costs per apron.

**1. Calculate total fixed costs:**
- Sewing machine: $85
- Other sewing tools: $32

Total fixed costs = $85 + $32 = $117

**2. Calculate the variable costs per apron:**
- Fabric for each apron: $16

**3. Determine the price Ron sells each apron for:**
- Selling price per apron: $25

**4. Calculate the profit per apron:**
Profit per apron = Selling price - Variable cost
Profit per apron = $25 - $16 = $9

**5. Set up the equation to find the number of aprons (x) he needs to sell to cover his total costs:**
Total sales = Total expenses
\[
25x = 117 + 16x
\]

**6. Solve for x:**
Subtract \(16x\) from both sides:
\[
25x - 16x = 117
\]
\[
9x = 117
\]

Now divide both sides by 9:
\[
x = \frac{117}{9} = 13
\]

Therefore, Ron must sell **at least 13 aprons** for his sales to equal his expenses.