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*