Question

You’re trying to find the number of cups of fruit punch mix per 1 cup of water. What number can you divide 1
2
1
​
by to find 1 cup of water?

Elyse's Fruit Punch Recipe
÷
Water
(cups) Fruit Punch Mix
(cups)
1
2
1
​

10
3
​

1 ?

Answer 1

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**.