Monday, April 30, 2007

100 Vegetables for 100 Dollars

20 Brinjals cost $1; 1 cucumber costs $5; 1 coconut costs $1. You must purchase a combination of all these vegetables, the total number of vegetables should be 100 and also its cost should be $100. (i.e.) make a purchase of 100 vegetables whose cost is also $100.


Answer:

Most people would certainly lament over the fact that 3 unknowns are there but however, only 2 equations could be set-up and hence it cannot be solved. It is better to make an attempt before making any such decision. If we assign the required brinjals, cucumbers and coconuts as x, y, and z then we have

x/20 + 5y + z = 100 ...............(1)

x + y + z = 100 ...............(2)

(2)-(1) gives 19x/20 - 4y = 0.

19x/20 = 4y.

19x = 80y.

x/y = 80/19.

Since 80 and 19 are relatively prime to each other and also x+y+z=100 the least values of x and y should be 80 and 19 and therefore z=1. Hence the soultions are 80 brinjals,19 cucumbers and 1 coconut. Q.E.D.

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