To determine how much juice concentrate and water are used to make 18 cups of juice, we first need to understand the ratio of juice concentrate to water.
We know that for every 1/4 cup of juice concentrate, we mix it with 2 cups of water. Therefore, the total mixture (juice) from this ratio is:
\[ \text{Total mixture} = \text{juice concentrate} + \text{water} = \frac{1}{4} \text{ cup} + 2 \text{ cups} = 2.25 \text{ cups} \]
Now, we can set up a proportion to determine how many of these mixtures are needed to reach a total of 18 cups of juice.
Let \( x \) be the number of mixtures. Each mixture yields 2.25 cups of juice, so we have:
\[ x \times 2.25 = 18 \]
Now, we solve for \( x \):
\[ x = \frac{18}{2.25} = 8 \]
Now that we know we need 8 mixtures, we can calculate the total amount of juice concentrate and water used.
For the juice concentrate, we have:
\[ \text{Total juice concentrate} = 8 \times \frac{1}{4} = 2 \text{ cups} \]
For the water, we have:
\[ \text{Total water} = 8 \times 2 = 16 \text{ cups} \]
Therefore, to make 18 cups of juice, you will use:
- Juice concentrate: 2 cups
- Water: 16 cups
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