Question

there are100 people and 100 plates.among 100 people they are divided into three categories rich which take 2plates each,2 service class eat in 3 plates and 4 poor eat in 1 plate.calculate no of persons of each categories?

Answer 1

We have x rich people, y service and z poor

And we have a system of 2 equations:

$x+y+z=100$

$2x+3/2y+z/4=100$

Which have this solutions

$y=60-7x/5$

$z=40+2x/5$

x,y,z should be integer and between 0 and 100. So we will have this possible options

1) $x=10, y=46, z=44$

2) $x=20, y=32, z=48$

3) $x=30, y=18, z=52$

4) $x=40, y=4, z=56$

Others won't be accepted because y should be divisible by 2, and z should be divisible by 4.