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?

To determine how many aprons Ron must sell for his sales to equal his expenses, we first need to calculate his total expenses and then set up an equation based on his sales. 1. **Calculate Total Expenses:** - Cost of sewing machine: \( \$ 85 \) - Cost of other sewing tools: \( \$ 32 \) - Cost of fabric per apron: \( \$ 16 \) The total fixed expenses (sewing machine and tools) are: \[ 85 + 32 = 117 \] Let \( x \) be the number of aprons Ron sells. The variable cost for fabric for \( x \) aprons is: \[ 16x \] Therefore, the total expenses can be expressed as: \[ \text{Total Expenses} = 117 + 16x \] 2. **Calculate Total Sales:** Ron sells each apron for \( \$ 25 \). Thus, the total sales from selling \( x \) aprons is: \[ \text{Total Sales} = 25x \] 3. **Set Up the Equation:** To find the number of aprons Ron needs to sell for his sales to equal his expenses, we set the total sales equal to the total expenses: \[ 25x = 117 + 16x \] 4. **Solve for \( x \):** Subtract \( 16x \) from both sides: \[ 25x - 16x = 117 \] \[ 9x = 117 \] Now, divide both sides by \( 9 \): \[ x = \frac{117}{9} = 13 \] Thus, Ron must sell **13 aprons** for his sales to equal his expenses.