# Thread: [SOLVED] An interrelated father, mother and children age question

1. ## [SOLVED] An interrelated father, mother and children age question

Hi all,
I am having difficulties with this question and would like to ask for some pointers

I understand that the parents ages will increase by [2 x number of years passed], but cannot factor this somehow into the sum of the children's ages

In 1992, a father's age added to that of his wife was ten times the sum of the ages of their children. In 1994, it was only six times the sum, and in 2000 it had fallen to three times the sum.
How many children do they have?

Any pointers would be greatly appreciated!!

2. Originally Posted by lindah
In 1992, a father's age added to that of his wife was ten times the sum of the ages of their children.
In 1994, it was only six times the sum, and in 2000 it had fallen to three times the sum.
How many children do they have?
f = father, w = wife, n = number of children, x = sum of children's ages in 1992

1992: f + w = 10x [1]

1994: f + w + 4 = 6(x + 2n) ; f + w = 6x + 12n - 4 [2]

2000: f + w + 16 = 3(x + 8n) ; f + w = 3x + 24n - 16 [3]

[1][2]: 6x + 12n - 4 = 10x ; x = 3n - 1 [4]

[1][3]: 3x + 24n - 16 = 10x ; x = (24n - 16) / 7 [5]

[4][5]: 3n - 1 = (24n - 16) / 7
21n - 7 = 24n - 16
3n = 9
n = 3 : so they have 3 children

All ok ?

3. Thank you so much!!
It makes sense now

I kept trying to reason [6x + expression] when I should have expressed it as x + 2n then times by 6.