Index

# The Fruit Vendor Problem

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:

0.5 pounds   =   W pounds
2%              100%

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.

oooooooooo
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oooooooooo
oooooooooo
oooooooooo
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oooooooooo
oooooooooo
oooooooooo
ooooooooo
x

What is a pound? A pound is 0.454 Kg. Most scientific work in the United States uses the metric system, but the old English system predominates in commerce. Various attempts at adopting the metric system have failed because of the cost involved in the conversion of highway signs, scales, odometers, machine parts, maps, etc. Globalization is providing some incentives toward adoption of the metric system. Soft drinks, for example, are sold in 2-liter bottles, and some car parts are now fabricated to metric specifications.