The Fruit Vendor
A fruit vendor bought 100 pounds of berries for $2.00 per pound and expected to double his investment by selling the berries for $4.00 per pound at an open-air market. The vendor only managed to sell 50 pounds of berries the first day and he sold the remainder on the second day. The fresh berries had a content of 99% water, but because of the hot weather, the berries dehydrated and contained only 98% water on the second day. How much profit did the vendor make?
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:
W = (0.5×100)/2 = 25 pounds
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.
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