SOLUTION: The sum of the ages of husband & his wife is four times the sum of the agesof their children . four years ago , the ratio of sum of their ages to the sum of their children was 18:

Question 1128046: The sum of the ages of husband & his wife is four times the sum of the agesof their children . four years ago , the ratio of sum of their ages to the sum of their children was 18:1 . two years hence the ratio will be 3:1 .how many children do they have ?
Found 2 solutions by ankor@dixie-net.com, josmiceli:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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.
=
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.
=
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.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = sum of husband and wife's ages
Let = sum of their children's ages
Let = the number of children
--------------------
(1)
(2)
(3)
( note that each parent and each child's age get
added to by number of years in future. The
opposite is true going into past )
------------------------------------------
(2)
(2)
(2)
Plug (1) into (2)
(2)
(2)
(2)
-------------------------------
(3)
(3)
(3)
(3)
(3)
-------------------------------
Multiply both sides of (3) by
and subtract (3) from (2)
(2)
(3)
-------------------------------

and

------------------
(3)
(3)
(3)
(3)
(3)
(3)
They have 4 children
-----------------------------
check:
(2)
(2)
(2)
(2)
(2)
(2)
OK
Get a 2nd opinion if this is incorrect

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