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Alec makes jam to sell at a local farmers' market. To make last week's batch, he used 2 cups of sugar and 18 cups of berries. It was so popular that he made a larger batch this week. To make this week's batch, Alec used 4 cups of sugar and 30 cups of berries, and the jam sold out even faster. Which batch had a greater ratio of sugar to berries?Last week's batch had a greater ratio.This week's batch had a greater ratio.Neither. The batches had the same ratio.Submit

Question

Alec makes jam to sell at a local farmers' market. To make last week's batch, he used 2 cups of sugar and 18 cups of berries. It was so popular that he made a larger batch this week. To make this week's batch, Alec used 4 cups of sugar and 30 cups of berries, and the jam sold out even faster. Which batch had a greater ratio of sugar to berries?Last week's batch had a greater ratio.This week's batch had a greater ratio.Neither. The batches had the same ratio.Submit

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Solution

To determine which batch had a greater ratio of sugar to berries, we need to calculate the ratio for each batch separately.

For last week's batch, the ratio of sugar to berries is 2 cups of sugar to 18 cups of berries. This simplifies to 1:9 when we divide both numbers by 2.

For this week's batch, the ratio of sugar to berries is 4 cups of sugar to 30 cups of berries. This simplifies to 2:15 when we divide both numbers by 2.

To compare these ratios, we need to convert them to a common denominator. The easiest way to do this is to convert them to a decimal or a fraction.

The decimal for last week's ratio is 1 ÷ 9 = 0.1111.

The decimal for this week's ratio is 2 ÷ 15 = 0.1333.

Therefore, this week's batch had a greater ratio of sugar to berries.

This problem has been solved

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