Question

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.
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.