Question 1128046
let p = the sum of the parents ages now
let s = the sum of the children's ages now
let c = no. of children
:
 The sum of the ages of husband & his wife is four times the sum of the ages of their children
p = 4s
 Four years ago, the ratio of sum of their ages to the sum of their children was
 18:1.
{{{(p-8)/(s-4c)}}} = {{{18/1}}}
cross multiply
p - 8 = 18(s-4c)
p - 8 = 18s - 72c
replace p with 4s, from the first statement
4s - 8 = 18s - 72c
72c = 18s - 4s + 8
72c = 14s + 8
7
  Two years hence the ratio will be 3:1.
{{{(p+4)/(s + 2c)}}} = {{{3/1}}}
Cross multiply
p + 4 = 3(s + 2c)
p + 4 = 3s + 6c
replace p with 4s
4s + 4 = 3s + 6c
4s - 3s = 6c - 4
s = 6c - 4
In the 2nd simplified equation, replace s with (6c-4)
72c = 14(6c-4) + 8
72c = 84c - 56 + 8
72c - 84c = -48
-12c = -48
c = -48/-12
c = 4 children is what they have
:
:
you can confirm this by finding p and s and checking the ratios with these values
s = 6(4) - 4
s = 20 is the sum of the children's ages
and
p = 4(20)
p = 80 is sum of the parents
:
I'll let you confirm this.