Question

4. Suppose that you have an enormous grapefruit that is 92% water (by weight). The grapefruit weights 100 pounds. If the water content of the grapefruit evaporates until it is 90% water (by weight), then approximately how much does the grapefruit now weigh?

Answer 1

Answer:

80 pounds.

Step-by-step explanation:

Let W₁ be the initial weight of water in the grapefruit, W₂ be the weight of water in the grapefruit after evaporation, and M be the total weight of the grapefruit after evaporation. Assuming that, originally, the grapefruit weighed 100 pounds with a 92% water content and the weight of the "non-water" part of the fruit (100 - W₁) does not change. The final weight of the grapefruit (M) is given by:

$W_1=0.92*100=92\\W_2=0.90*M\\W_2+(100-W_1) = M\\W_2=M-8\\(1-0.9)M=8\\M=80$

The grapefruit now weighs 80 pounds.