Max is starting a tropical soda stand. Empty bottles cost $0.32 each and ingredients
cost $0.10 per bottle. Additionally, Max spent $54 on a bottle-cap sealer. He will sell his soda for $1.50 per bottle.
How many bottles of soda must Max sell for his sales to equal his expenses?

To solve this, we need to set up an equation based on Max's expenses and sales, and then solve for the number of bottles of soda he needs to sell to break even.

### Breakdown of costs:
1. **Cost per bottle**:
   - Each empty bottle costs $0.32.
   - Ingredients per bottle cost $0.10.
   - So, the total cost per bottle = $ 0.32 + 0.10 = 0.42 $ dollars per bottle.
  
2. **Fixed cost**:
   - Max spent $54 on a bottle-cap sealer, which is a one-time fixed cost.

3. **Revenue per bottle**:
   - Max will sell his soda for $1.50 per bottle.

Let the number of bottles Max needs to sell be $ x $.

### Total cost:
- The variable cost for $ x $ bottles is $ 0.42x $ (since each bottle costs $0.42 to produce).
- The fixed cost is $54.

So, the total cost is:
\[
\text{Total cost} = 0.42x + 54
\]

### Total revenue:
- Max earns $1.50 for each bottle sold, so the total revenue for $ x $ bottles is:
\[
\text{Total revenue} = 1.50x
\]

### Break-even point:
To break even, the total revenue must equal the total cost:
\[
1.50x = 0.42x + 54
\]

Now, solve for $ x $:

1. Subtract $ 0.42x $ from both sides:
   \[
   1.50x - 0.42x = 54
   \]
   \[
   1.08x = 54
   \]

2. Divide both sides by 1.08:
   \[
   x = \frac{54}{1.08} = 50
   \]

### Conclusion:
Max must sell **50 bottles** of soda for his sales to equal his expenses.

Would you like more details or have any questions?

---

Here are 5 related questions:
1. What if the empty bottles cost $0.40 each, how would that affect the number of bottles needed to break even?
2. How much profit will Max make if he sells 100 bottles?
3. What if Max decides to sell the soda at $2 per bottle, how many bottles will he need to sell to break even?
4. How would Max's break-even point change if the bottle-cap sealer cost $75 instead of $54?
5. If Max reduces the ingredients cost to $0.08 per bottle, how many bottles must he sell to break even?

**Tip:** When solving break-even problems, always carefully separate variable costs and fixed costs to set up a clear equation.

Max is starting a tropical soda stand. Empty bottles cost $0.32 each and ingredients cost $0.10 per bottle. Additionally, Max spent $54 on a bottle-cap sealer. He will sell his soda for $1.50 per bottle. How many bottles of soda must Max sell for his sales to equal his expenses?

Discover how to calculate the break-even point for Max's tropical soda stand. With costs for bottles and ingredients and a fixed expense for a bottle-cap sealer, learn how many bottles Max needs to sell at $1.50 each to cover his expenses. Perfect for students in Grades 6-8.

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