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.
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Convert 2.5 cups of soda to an improper fraction: \[ 2.5 = \frac{25}{10} = \frac{5}{2} \]
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Now, we want to find the ratio of soda to pineapple juice: \[ \text{Ratio of soda to pineapple juice} = \frac{\text{soda}}{\text{pineapple juice}} = \frac{\frac{5}{2}}{\frac{2}{5}} \]
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To divide fractions, we multiply by the reciprocal of the second fraction: \[ \frac{5}{2} \div \frac{2}{5} = \frac{5}{2} \times \frac{5}{2} = \frac{25}{4} \]
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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.