Question

Start by finding the unit rate for Elyse’s recipe. You need to find the number of cups of fruit punch mix per 1 cup of water. What can you divide 1
2
1
​
cups of water 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 unit rate of Elyse's fruit punch recipe, you want to determine how many cups of fruit punch mix are used per 1 cup of water.

The recipe states that for \( \frac{1}{2} \) cups of water, you need \( 10/3 \) cups of fruit punch mix.

To find out how many cups of fruit punch mix you would need for 1 cup of water, you can set up a proportion. Since you're starting with \( \frac{1}{2} \) cups and want to scale it up to 1 cup, you can find out what you need to multiply \( \frac{1}{2} \) by to get 1.

To find this multiplier, you can do:

\[
1 \div \frac{1}{2} = 1 \times \frac{2}{1} = 2
\]

So, you need to multiply both the cups of water and the cups of fruit punch mix by 2.

Now, we can find the amount of fruit punch mix needed for 1 cup of water:

\[
\text{Fruit Punch Mix for 1 cup of water} = \frac{10}{3} \text{ cups} \times 2 = \frac{20}{3} \text{ cups}
\]

Thus, for 1 cup of water, you would need \( \frac{20}{3} \) cups of fruit punch mix.

To summarize:
- **1 cup of water requires \( \frac{20}{3} \) cups of fruit punch mix.**