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
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?
Solution
To determine which batch of jam tasted more like cranberries, we need to calculate the ratio of cranberries to total fruit in each batch.
For the first batch: The total amount of fruit is 3 cups of cranberries + 5 cups of pears = 8 cups. The ratio of cranberries to total fruit is therefore 3/8.
For the second batch: The total amount of fruit is 5 cups of cranberries + 8 cups of pears = 13 cups. The ratio of cranberries to total fruit is therefore 5/13.
Comparing these ratios, 3/8 is greater than 5/13. Therefore, the first batch of jam tasted more like cranberries.
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