https://file.aiquickdraw.com/mathbot/file/1726205980037xpshbdl9.jpg

The image provides the following details regarding the production costs of an item:

- **Fixed cost**: $4,665
- **Variable cost per item**: $37.50
- **Price at which the item is sold**: $37.80

We can analyze this information to determine the break-even point (the number of items that need to be sold to cover all costs).

### Break-even Point Formula:
\[
\text{Break-even point} = \frac{\text{Fixed costs}}{\text{Price per item} - \text{Variable cost per item}}
\]

Substituting the values:
\[
\text{Break-even point} = \frac{4665}{37.80 - 37.50}
\]

Let me calculate that for you.The break-even point is approximately **15,550 items**. This means the company needs to sell about 15,550 items to cover both fixed and variable costs and start making a profit.

Would you like more details on this, or have any questions?

Here are 5 related questions for further exploration:

1. How would a change in the variable cost impact the break-even point?
2. What if the selling price were reduced—how would that affect profitability?
3. How much profit would be earned if 20,000 items were sold?
4. What is the contribution margin per item in this scenario?
5. Can this approach be used to evaluate profit margins for other products?

**Tip:** In break-even analysis, the smaller the gap between selling price and variable cost, the higher the number of items needed to break even.

The fixed and variable costs to produce an item are given along with the price at which an item is sold: Fixed cost: $4665, Variable cost per item: $37.50, Price at which the item is sold: $37.80. How many items need to be sold to break even?

Learn how to calculate the break-even point given a fixed cost of $4665, variable cost per item of $37.50, and selling price of $37.80. Understand the break-even formula and solve this business-related algebra problem step by step. Suitable for Grades 9-12.

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