SOLUTION: The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34. Find the age of the son and Father.
The sum of the present ages of t
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Question 888285: The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 34. Find the age of the son and Father.
The sum of the present ages of the father and the son is 56 years. 4 years hence, the son’s age will be 1/3 that of the father. What are the present ages of the father and the son?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 = (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?
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