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 was unable to sell any of the berries the first few

days, but he eventually sold them all. The fresh berries

had a content of 99% water, but because of the hot weather,

all the berries that sold were dehydrated and contained

only 98% water. How much profit did the vendor make?

 

 

 

 

 

 

 

Answer:

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

After the berries sat for a while, they only had a water content of 98%. The weight of the dehydrated berries can be calculated as follows:

The  100 pounds of berries with 99% water had 1% of non-water components which weighed 1 pound (100 pounds × 1/100 = 1 pound).

When the berries dehydrate, the weight of the non-water component is still 1 pound 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:

1 pound = W (pounds)
 2%        100% 

W (pounds) = (1 pound × 1.00) / .02

W = 50 pounds

What used to be 100 pounds of berries with 99% water content are now 50 pounds of berries with 98% water content.

The sale of berries with 98% water is: 50 pounds × $4.00/pound = $200.00. The profit is the total sales ($200.00) minus the cost ($200.00). The vendor had a $0.00 dollar profit!

The loss of water is a loss of profits.

This is why supermarkets spray water on fresh vegetables and keep produce refrigerated!

ALSO, THINK OF WHAT DEHYDRATION DOES TO YOU...

A SEEMINGLY LOW LOSS OF WATER CONTENT CAN REPRESENT BIG TROUBLE!