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

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.