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
​

8
1
​

1 ?

Answer 1

To find the unit rate for Elyse's recipe, you want to determine how much fruit punch mix is used per 1 cup of water.

Elyse’s recipe indicates that she uses \( \frac{1}{2} \) cup of water and \( 8 \) cups of fruit punch mix.

To find out how much fruit punch mix corresponds to \( 1 \) cup of water, you can set up the following proportion based on the original amounts used in the recipe:

\[
\text{If} \; \frac{1}{2} \; \text{cup of water uses} \; 8 \; \text{cups of mix, then} \; 1 \; \text{cup of water uses} \; x \; \text{cups of mix}.
\]

You can solve for \( x \):

\[
\frac{1}{2} \text{ cups of water} \rightarrow 8 \text{ cups of fruit punch mix}
\]

To find \( x \) when the water is \( 1 \) cup:

\[
\frac{1}{2} : 8 = 1 : x
\]

Cross-multiplying gives:

\[
\frac{1}{2}x = 8
\]

Now solve for \( x \):

\[
x = 8 \times 2
\]
\[
x = 16
\]

Thus, the unit rate is \( 16 \) cups of fruit punch mix for \( 1 \) cup of water.

In conclusion:

**For every 1 cup of water, you need 16 cups of fruit punch mix.**