SOLUTION: a man is now 5 times as old as his son . Four years ago, the product of their ages was 52 . Find their present ages

Question 892243: a man is now 5 times as old as his son . Four years ago, the product of their ages was 52 . Find their present ages

Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
set m = man's age
s = son's age
m = 5s
(m-4)(s-4) = 52
substitute 5s for m in the above
(5s-4)(s-4) = 52
5s^2 -20s -4s + 16 = 52
5s^2 -24s + 16 = 52
add -54 to each side
5s^2 -24s -36 = 0
We want two numbers whose product is -180 and whose sum is -24.
-30 and 6 work for this.
5s^2 -30s +6s -36 = 0
factor by grouping
5s(s - 6) +6(s - 6) = 0
(5s + 6)(s - 6) = 0
So 5s + 6 = 0 or s - 6 = 0
For 5s + 6 = 0 , add -6 to each side
5s = -6
divide each side by 5
s = -6/5
For s -6 = 0
add 6 to each side
s = 6
We need a positive number so the son's age is 6
Since m = 5s , m = 5(6) = 30
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