Question

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?

Answer 1

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.