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The problem involves determining the break-even point for producing and selling 3-pack sets of Easy Fly hacky sacks.

We are given:
1. **Cost equation**: \( y = 1.35x + 72.6 \), where \( x \) represents the number of 3-pack sets produced.
2. **Revenue equation**: \( y = 3.55x \), where \( x \) is the number of 3-pack sets sold.

### To find the break-even point:
The break-even point occurs when **cost = revenue**, meaning we set the two equations equal to each other:

\[
1.35x + 72.6 = 3.55x
\]

### Solving for \( x \):
\[
3.55x - 1.35x = 72.6
\]
\[
2.2x = 72.6
\]
\[
x = \frac{72.6}{2.2} = 33
\]

Thus, the break-even point is when **33 sets of 3-pack Easy Fly hacky sacks are produced and sold**.

### Follow-up questions:
1. What does the slope of the cost equation represent in this context?
2. How does the fixed cost of 72.6 affect the profitability of the hacky sacks?
3. How would the break-even point change if the cost per set increased by 0.50?
4. How can the company reduce its break-even point?
5. If the revenue per pack increased to 4.00 per pack, what would the new break-even point be?

#### Tip: Always keep fixed and variable costs in mind when calculating break-even points for different scenarios.

A hacky sack manufacturer has just released a 3-pack of the Easy Fly hacky sacks. The cost to manufacturer each 3-pack of the Easy Fly is y = 1.35x + 72.6. The revenue is y = 3.55x. What is the break-even point for a 3-pack of Easy Fly hacky sacks?

Learn how to calculate the break-even point for manufacturing 3-packs of Easy Fly hacky sacks using linear equations. This problem covers key algebra concepts, including cost and revenue equations, and teaches students how to solve for the break-even point. Suitable for Grades 9-11.

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