The Fruit Vendor

The decrease of water content from 99% to 98% may seem insignificant, but it reduces the weight of the fruit by 50%. The 1% decrease in water content of the fruit should not be confused with a 1% decrease of the total amount of water, which would indeed be small.

The cost of the berries is:   100 pounds × $2.00/pound = $200.00

The first day sale of berries with 99% water is: 50 pounds × $4.00/pound = $200.00. The vendor covers his cost on the first day, but does not make a profit.

On the second day, the berries have a water content of 98%. The weight of the dehydrated berries can be calculated as follows:

The leftover 50 pounds of berries with 99% water have 1% of non-water components which weigh 0.5 pound (50 pounds × 1/100 = 0.5 pounds).

When the berries dehydrate, the weight of the non-water component is still 0.5 pounds but it now comprises 2% of the total weight of the dehydrated fruit with the other 98% being water. The weight, W, of the dehydrated fruit can be calculated as follows:

What used to be 50 pounds of berries with 99% water content are now 25 pounds of berries with 98% water content.

The second day sale of berries with 98% water is: 25 pounds × $4.00/pound = $100.00. The profit is the total sales ($300.00) minus the cost ($200.00). The vendor had a $100.00 Dollar profit. The loss of water is also a loss of profits. This is why supermarkets spray water on fresh vegetables and keep produce refrigerated.

Dehydration is illustrated graphically with 100 cells, where each o represents water and x represents the non-water portion. The x is only 1% of the total number of cells, but 2% of the bottom 50 cells (highlighted in red). The 50 black o‘s represent water lost by dehydration.