Subjects algebra

Iced Coffee Mix

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Iced Coffee Mix


1. **State the problem:** Jomar wants to make 1-liter bottles of iced coffee mix using 3/4 liter of brewed coffee and 1/2 liter of milk per bottle. He has 3 liters of coffee and 2 liters of milk available. 2. **Define variables and equations:** Let $x$ be the number of 1-liter bottles he can make. Since each bottle requires $\frac{3}{4}$ liter of coffee, total coffee used is $\frac{3}{4}x$ liters. Since each bottle requires $\frac{1}{2}$ liter of milk, total milk used is $\frac{1}{2}x$ liters. 3. **Set up constraints based on available ingredients:** $\frac{3}{4}x \leq 3$ (coffee constraint) $\frac{1}{2}x \leq 2$ (milk constraint) 4. **Solve inequalities:** From coffee: $x \leq \frac{3}{(3/4)} = \frac{3}{0.75} = 4$ From milk: $x \leq \frac{2}{(1/2)} = \frac{2}{0.5} = 4$ 5. **Determine the maximum full bottles:** The limiting factor is the smaller maximum $x$, which is 4. Jomar can make 4 full 1-liter bottles of iced coffee mix. **Final answer:** $$x = 4$$ bottles.