Bot GPT 4-o mini To find the number of cups of fruit punch mix per 1 cup of water in Elyse's fruit punch recipe, we can set up a proportion based on the provided information.
From the recipe:
- For \( \frac{1}{2} \) cup of water, there are 10 cups of fruit punch mix.
- We want to find out how many cups of fruit punch mix are needed for 1 cup of water.
We can set up the following proportion based on the relationship of water to fruit punch mix:
\[ \frac{\text{Fruit Punch Mix}}{\text{Water}} = \frac{10 \text{ cups}}{\frac{1}{2} \text{ cup}} \]
Now we want to find out how many cups of fruit punch mix (let's call it \( x \)) are needed for 1 cup of water:
\[ \frac{x \text{ cups}}{1 \text{ cup}} = \frac{10 \text{ cups}}{\frac{1}{2} \text{ cup}} \]
Cross-multiplying gives us:
\[ x \cdot \frac{1}{2} = 10 \]
To solve for \( x \), multiply both sides by 2:
\[ x = 10 \times 2 \] \[ x = 20 \]
So, for 1 cup of water, you would need 20 cups of fruit punch mix.
1 answer