Question 888285
let f = father's age
let s = son's age
:
Write an equation for each statement
:

The sum of the ages of a father and his son is 45 years.
f + s = 45
s = (45-f)
:
 Five years ago, the product of their ages was 34.
(f-5)*(s-5) = 34
replace s with (45-f)
(f-5)*(45-f-5) = 34
(f-5)*(-f+40) = 34
FOIL
-f^2 + 40f + 5f - 200 - 34 = 0
-f^2 + 45f - 234 = 0
Multiply by -1
f^2 - 45f + 234 = 0
Factors to
(f-39)(f-6) = 0
Two solutions
f = 39 yrs is fathers age, other solution unreasonable
Find son's age
s = 45 - 39
s = 6 yrs is the son's age
:
Confirm this; 5 yrs ago, 34 * 1 = 34
:
:
The sum of the present ages of the father and the son is 56 years.
f + s = 56
f = (56 - s)
:
4 years hence, the son’s age will be 1/3 that of the father.
s + 4 = {{{1/3}}}(f + 4)
multiply both sides by 3
3(s + 4) = f + 4
3s + 12 = f + 4
3s = f + 4 - 12
3s = f - 8
replace f with (56-s)
3s = 56 - s - 8
3s + s = 48
4s = 48
s = 48/4
s = 12 yrs is son's age
I'll let you find father's age, check solution in given statements



 What are the present ages of the father and the son?