100 vegetables for $100

by R. Kesavan
(Madras, TamilNadu, India)

20 brinjals cost $1; 1 pumpkin costs $5; 1 coconut costs $1. Try to purchase 100 vegetables for $100.

Solution:

If 'x','y', and 'z' are the required numbers of brinjals, pumpkin and coconut then the following equations can be built:

x/20 +5y + z = 100 .............(1)
x + y + z = 100 .............(2)

(1)-(2) gives, -19x/20 +4y = 0
-19x/20 = -4y
19x=80y
x/y=80/19

The number of brinjals and the number of pumpkin should be in the ratio 80:19. Since 80 and 19 have no common factors and x+y should be below 100, they must be 80 and 19 respectively.
Therefore the number of brinjals is 80, the number of pumpkins is 19, and the number of cococut is 1.

Q.E.D.