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?
Answers
GPT-4o mini
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.
\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{5}{2} \text{ cups of soda}
\]
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.