1. **State the problem:** Max wants to find out how many bottles of soda he must sell so that his total sales equal his total expenses. 2. **Define variables and costs:** Let $x$ be the number of bottles sold. - Cost per empty bottle: $0.32$ - Cost per bottle ingredients: $0.10$ - Fixed cost for bottle-cap sealer: $54$ - Selling price per bottle: $1.50$ 3. **Write the total cost (expenses) equation:** $$\text{Total expenses} = 0.32x + 0.10x + 54 = 0.42x + 54$$ 4. **Write the total sales equation:** $$\text{Total sales} = 1.50x$$ 5. **Set sales equal to expenses to find break-even point:** $$1.50x = 0.42x + 54$$ 6. **Solve for $x$:** $$1.50x - 0.42x = 54$$ $$1.08x = 54$$ 7. **Divide both sides by 1.08:** $$x = \frac{54}{1.08}$$ $$x = \cancel{\frac{54}{1.08}} = 50$$ 8. **Interpretation:** Max must sell **50 bottles** of soda to cover all his expenses. **Final answer:** $$\boxed{50}$$