Beth makes keychains using a 3D printer and sells them for $3 each. To set up her business, she spent $224 on her 3D printer and $100 on a website. Each keychain costs $0.75 in materials to make.

Question

How many keychains must Beth sell for her sales to equal her expenses?
keychains

Answer 1

To find out how many keychains Beth must sell for her sales to equal her expenses, we start by calculating her total fixed expenses and her variable costs.

1. Calculate fixed expenses:

   • Cost of the 3D printer: $224
   • Cost of the website: $100
   • Total fixed expenses: \( 224 + 100 = 324 \) dollars

2. Calculate variable expenses per keychain:

   • Cost of materials per keychain: $0.75

3. Calculate the selling price per keychain:

   • Selling price per keychain: $3.00

4. Determine the profit per keychain: The profit per keychain is the selling price minus the variable cost: \[ \text{Profit per keychain} = \text{Selling price} - \text{Variable cost} = 3.00 - 0.75 = 2.25 \text{ dollars} \]

5. Set up the equation for total profit to equal total expenses: Let \( x \) be the number of keychains sold. The total profit from selling \( x \) keychains will be the profit per keychain multiplied by the number of keychains: \[ 2.25x = 324 \]

6. Solve for \( x \): \[ x = \frac{324}{2.25} \]

   Calculating this gives: \[ x = 144 \]

Therefore, Beth must sell 144 keychains for her sales to equal her expenses.