To find the unit rate of soda to pineapple juice in the punch, we first need to convert the quantities into a simpler form. The recipe states that there are 2 1/2 cups of soda, which can be expressed as:
\[ 2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2} \text{ cups of soda} \]
We also have 2/5 of a cup of pineapple juice.
Now, we want to find the ratio of soda to pineapple juice:
\[ \text{Ratio} = \frac{\text{Soda}}{\text{Pineapple Juice}} = \frac{\frac{5}{2}}{\frac{2}{5}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ = \frac{5}{2} \times \frac{5}{2} = \frac{25}{4} \]
This means that the unit rate of soda to pineapple juice is \( \frac{25}{4} \) cups of soda for every cup of pineapple juice.
To express it as a simpler ratio, we can also represent it as:
\[ 25:4 \]
This indicates that for every 4 cups of pineapple juice, there are 25 cups of soda.