Let the number of children = x
the number of young people = y
the number of old people = z
x + y + z = 100
4x + 2y + 0.25z = 100
There is no third equation, which makes it difficult to solve but we have a condition that x, y and z are all integers as we can't have 1.7 children.
x + y +z = 100
⇒x = 100- y - z
Putting x in second equation
4(100-y-z) + 2y + 0.25z = 100
⇒400 - 4y - 4z + 2y + 0.25 z = 100
⇒2y + 3.75z = 300
Now I will solve by hit-and-trial method keeping certain points in mind.
1. Take only integral values of y.
2. z is an integer. So
is an integer or (300-2y) is a multiple of 3.75.
3. (300-2y) will always be an even integer.
4. An even integer which is a multiple of 3.75 should be an multiple of 30.(This is an important conclusion to reduce the calculation).
5. After you get a answer, check it all conditions are satisfied.
6.Value of z is greater than x and y.
(If you don't understand any point, ask)
take y = 15, so that 2y = 30 is a multiple of 30 and (300-30)=270 is also a multiple of 30.
then z = 270/3.75 = 72
x = 100-72-15 = 13
x+y+z = 100(satified)
Answer in the first attempt!!!
young people = 15
old people = 72