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


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there are 5 children in the family.