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.