SOLUTION: 2 yrs. ago a man's age was 3 times the square of his son's age . 3 yrs. hence his age will be 4 times his son's age. Find their present ages

Question 333772: 2 yrs. ago a man's age was 3 times the square of his son's age . 3 yrs. hence his age will be 4 times his son's age. Find their present ages
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let m = man's present age
Let s = son's present age
:
Write an equation for each statement:
:
"2 yrs. ago a man's age was 3 times the square of his son's age."
m - 2 = 3(s - 2)^2
:
FOIL (s-2)(s-2)
m - 2 = 3(s^2 - 4s + 4)
m - 2 = 3s^2 - 12s + 12
m = 3s^2 - 12s + 12 + 2
m = 3s^2 - 12s + 14
:
"3 yrs. hence his age will be 4 times his son's age."
m + 3 = 4(s + 3)
m + 3 = 4s + 12
m = 4s + 12 - 3
m = 4s + 9
:
Find their present ages
Replace m with (4s+9) in the 1st equation
4s + 9 = 3s^2 - 12s + 14
0 = 3s^2 - 12s - 4s + 14 - 9
0 = 3s^2 - 16s + 5
Factors to
(3s - 1)(s - 5) = 0
s = 5 yrs is the reasonable answer for son's present age
:
Find M using m = 4s + 9
m = 4(5) + 9
m = 29 yrs, man's present age
;
:
Check solution in the the statement:
"2 yrs. ago a man's age was 3 times the square of his son's age "
29 - 2 = 3(5-2)^2
27 = 3(3^2); confirms our solutions

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