SOLUTION: The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age that time. The present age of father and son, respect

Question 964046: The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age that time. The present age of father and son, respectively are?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let f = father's present age
let s = son's
:
Write an equation for each statement.
:
The sum of the ages of a father and son is 45 years.
f + s = 45
s = (45-f)
:
Five years ago, the product of their ages was four times the father's age that time.
(f-5)*(s-5) = 4(f-5)
Replace s with (45-f)
(f-5)*((45-f)-5) = 4f - 20
(f-5((-f+40) = 4f - 20
FOIL
-f^2 + 40f + 5f - 200 = 4f - 20
combine like terms on the left
-f^2 + 45f - 4f - 200 + 20 = 0
-f^2 + 41f - 180 = 0
multiply by -1, easier to factor
f^2 - 41f + 180 = 0
Factors to
(f-5)(f-36) = 0
f = 36 yrs, only reasonable answer for the father's age
then
s = 45 - 36
s = 9 yrs is the son's age
:
:
Let's see if that works in the statement:
"Five years ago, the product of their ages was four times the father's age that time."
Dad was 31, son was 4
31 * 4 = 4(31)

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