Question

A punch recipe requires 2/5 of a cup of pineapple juice for every 2 1/2 cups of soda. What is the unit rate of soda to pineapple juice in the punch?

Answer 1

To find the unit rate of soda to pineapple juice in the punch, we first need to express everything in terms of a single unit. The punch recipe requires:

- 2/5 cup of pineapple juice
- 2.5 cups of soda

We can find the unit rate by comparing the amount of soda to the amount of pineapple juice.

1. **Convert 2.5 cups of soda to an improper fraction:**
\[
2.5 = \frac{25}{10} = \frac{5}{2}
\]

2. **Now, we want to find the ratio of soda to pineapple juice:**
\[
\text{Ratio of soda to pineapple juice} = \frac{\text{soda}}{\text{pineapple juice}} = \frac{\frac{5}{2}}{\frac{2}{5}}
\]

3. **To divide fractions, we multiply by the reciprocal of the second fraction:**
\[
\frac{5}{2} \div \frac{2}{5} = \frac{5}{2} \times \frac{5}{2} = \frac{25}{4}
\]

4. **Evaluating this gives a unit rate of soda to pineapple juice:**
\[
\frac{25}{4} = 6.25
\]

Thus, there are 6.25 cups of soda for every cup of pineapple juice.

### Conclusion

The unit rate of soda to pineapple juice in the punch is **6.25:1**.