Question 537055
Let h = husbands present age 
Let w = wife's present age,
Let c = sum of children' age at this time
:
"the sum of ages of husband and his wife is four times the sum of ages of their children."
h + w = 4c
:
let n = number of children 
four years ago, the ratio of sum of their ages to the sum of ages of their children was 18:1.
{{{(h+w-8)/(c-4n)}}} = 18; (You subtract 4 for each person)
h+w-8 = 18(c-4n)
h+w-8 = 18c - 72n
h+w = 18c - 72n + 8
Replace h+w with 4c
4c = 18c - 72n + 8
4c - 18c = -72n + 8
-14c = -72n + 8
14c = 72n - 8; multiplied by -1
:
two years hence the ratio will be 3:1.
{{{(h+w+4)/(c+2n)}}} = 3
h + w + 4 = 3(c+2n)
h + w = 3c + 6n - 4
Replace h+w with 4c
4c = 3c + 6n - 4
4c - 3c = 6n - 4
c = 6n - 4
:
14c = 72n - 8
replace c with (6n-4)
14(6n-4) = 72n - 8
84n - 56 = 72n - 8
84n - 72n = -8 + 56
12n = 48
n = 48/12
n = 4 children
:
:
Check this: find c, 
c = 6(4) -4
c = 20; the sum of the children's ages
then
4(20) = 80 the sum of the parents ages
:
Use these values in the last statement:
two years hence the ratio will be 3:1.
{{{(80+4)/(20+2(4))}}} =  {{{(84)/(28)}}} = 3