Problema Solution
The sum of the parent's ages is twice the sum of their children's ages. Five years ago, the sum of the parent's ages is four times the sum of their children's ages. In fifteen years, the sum of the parent's ages will be equal to the sum of their children's ages. How many children were in the family?
Answer provided by our tutors
let
x = the number of children in the family
y = the sum of children's ages
z = the parents sum of ages
The sum of the parent's ages is twice the sum of their children's ages:
z = 2y
Five years ago, the sum of the parent's ages is four times the sum of their children's ages:
z - 2*5 = 4(y - 5x)
In fifteen years, the sum of the parent's ages will be equal to the sum of their children's ages:
z + 2*15 = y + 15x
by solving the system of equations:
z = 2y
z - 5 = 4(y - 5x)
z + 15 = y + 5x
we find:
x = 5 children
click here to see the step by step solution of the system of equations:
there are 5 children in the family.