SOLUTION: ``The sum of the ages of father and son is 45 years. 5 years ago the product of the of their ages was 4 times the father age at that time. Find their present ages .''.

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Question 188757: ``The sum of the ages of father and son is 45 years. 5 years ago the product of the of their ages was 4 times the father age at that time. Find their present ages
.''.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
``The sum of the ages of father and son is 45 years. 5 years ago the product of
the of their ages was 4 times the father age at that time. Find their present ages
:
Let f = father's present age
Let s = son's present age
:
Write an equation for each statement:
:
"``The sum of the ages of father and son is 45 years."
f + s = 45
or for substitution, we can say:
f = (45-s)
:
" 5 years ago the product of the of their ages was 4 times the father age at that time."
(f-5) * (s-5) = 4(f-5)
FOIL
fs - 5f - 5s + 25 = 4f - 20
Combine f on the left, s and numbers on the right
fs - 5f - 4f = 5s - 20 - 25
fs - 9f = 5s - 45
:
Factor out f:
f(s-9) = 5s - 45
;
divide both sides by (s-9)
f =
:
Substitute (45-s) for f
45 - s =
:
Multiply both sides by (s-9)
(-s + 45)(s-9) = 5s - 45
:
FOIL again
-s^2 + 9s + 45s - 405 = 5s - 45
;
Combine on left to form a quadratic equation
-s^2 + 54s - 5s - 405 + 45 = 0
-s^2 + 49s - 360 = 0
;
Multiply by -1 to change the signs, easier to factor
s^2 - 49s + 360 = 0
(s - 9) (s - 40) = 0
;
Most reasonable solution
s = 9 is the son's age,
Then
f = 45 - 9
f = 36 is the father's age
;
:
Check solution in the statement:
"5 years ago the product of the of their ages was 4 times the father age at that time.
31 * 4 = 4(31), confirms our solution
:
:
A lot of steps here, but each one should make sense to you. Let me know if
you have any questions about this. Carl