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The image shows a problem involving cost, revenue, and profit calculations related to selling keyboards.

Here is the problem statement from the image:

- **Cost per keyboard:** $40 per keyboard.
- **Selling price per keyboard:** $52 per keyboard.

The problem asks: **How many keyboards must be sold to earn a profit?**

### Solution:

To find the number of keyboards that must be sold to earn a profit, we need to set up an equation where the total revenue from selling the keyboards is greater than the total cost of producing them.

Let $ x $ be the number of keyboards sold.

- **Total cost** for $ x $ keyboards: $ \text{Cost} = 40x $
- **Total revenue** from selling $ x $ keyboards: $ \text{Revenue} = 52x $

To find the break-even point (where profit is zero), we set cost equal to revenue:
\[
40x = 52x
\]

However, for profit:
\[
\text{Revenue} > \text{Cost}
\]
\[
52x > 40x
\]

Simplifying this:
\[
52x - 40x > 0
\]
\[
12x > 0
\]

To make a profit, the number of keyboards $ x $ must be any positive integer because for every keyboard sold, there is a profit of $12.

### Conclusion:

Any number of keyboards sold beyond the break-even point will generate profit. However, at least **1 keyboard** must be sold to ensure a profit.

---

Would you like more details or have any questions? Here are five related questions to consider:

1. What if the cost per keyboard changes? How would that affect the number needed to make a profit?
2. How would the analysis change if there were additional fixed costs involved?
3. What if the selling price was less than the cost price? What would be the break-even point?
4. How does the concept of profit margin apply to this scenario?
5. How can this type of analysis be applied to other products or services?

**Tip:** Always consider fixed costs or other expenses when calculating profit, as they affect the total number of units needed to break even.

Wyatt buys $40 worth of materials to make beaded keychains. If Wyatt sells his keychains for $52 each, how many keychains must he sell to earn a profit?

Learn how to calculate the number of keychains Wyatt must sell to earn a profit. This problem involves basic algebraic concepts and profit calculation, suitable for students in Grades 6-8.

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