Every summer, Ronald makes cranberry-pear jam with the fruit he collects from his garden. Last summer, he used 3 cups of cranberries and 5 cups of pears to make his jam. This summer, Ronald decided to make an even larger batch using 5 cups of cranberries and 8 cups of pears. Which batch of jam tasted more like cranberries?

Question

GPT-4o mini · Answer

To determine which batch of jam tasted more like cranberries, we can calculate the ratio of cranberries to the total volume of fruit used in each batch.

Last summer's batch:

Cranberries: 3 cups
Pears: 5 cups
Total: 3 cups + 5 cups = 8 cups

The ratio of cranberries to the total fruit in the last summer's batch is: \[ \frac{3 \text{ cups of cranberries}}{8 \text{ cups of total fruit}} = \frac{3}{8} = 0.375 \]

This summer's batch:

Cranberries: 5 cups
Pears: 8 cups
Total: 5 cups + 8 cups = 13 cups

The ratio of cranberries to the total fruit in this summer's batch is: \[ \frac{5 \text{ cups of cranberries}}{13 \text{ cups of total fruit}} \approx \frac{5}{13} \approx 0.3846 \]

Comparison of the ratios:

Last summer's ratio: 0.375
This summer's ratio: approximately 0.3846

Since 0.3846 (this summer) is higher than 0.375 (last summer), the batch made this summer tasted more like cranberries compared to the last summer's batch.