Question

Grapes are 80% water by weight. When a bushel of grapes dries in the sun for two weeks, it loses 50% of its total weight. All of the weight loss is due to the loss of water. After drying for two weeks, what percentage of the grapes is water by weight? Express your answer to the nearest percent.

Answer 1

60%

Explanation:

Given grapes that are 80% water by weight lose 50% of their total weight when dried. You want to know want to know the percentage of a dried grape's weight that is water if all of the weight loss is due to water loss.

Dried grapes

Suppose a grape weighs one unit. Of that, 80% or 0.8 unit is water, so 0.2 unit is solids.

When 0.5 unit of water are lost, the dried grape consists of 0.2 unit of solids and (0.8 unit - 0.5 unit) = 0.3 unit of water. The total weight of the dried grape is half the original weight.

The fraction of a dried grape that is water is ...

(0.3 unit)/(0.5 unit) = 3/5 = 60%

A dried grape is 60% water by weight.

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