Let
$x$ = number of children in the family
$y$ = sum of parents' ages
$z$ = sum of children’s ages
The sum of the parents' ages is twice the sum of their children’s ages
$y = 2z$ → equation (1)
Five years ago, the sum of the parents' ages was four times the sum of their children’s ages
$y - 5(2) = 4(z - 5x)$
$y - 10 = 4z - 20x$
Substitute y = 2z
$2z - 10 = 4z - 20x$
$20x - 10 = 2z$
$z = 10x - 5$ → equation (2)
In fifteen years, the sum of the parents' ages will be equal to the sum of their children’s ages
$y + 15(2) = z + 15x$
$y + 30 = z + 15x$
Substitute y = 2z
$2z + 30 = z + 15x$
$z + 30 = 15x$
Substitute z = 10x – 5
$(10x - 5) + 30 = 15x$
$25 = 5x$
$x = 5$ answer
