SOLUTION: The father and the son together have 46 years. Three years ago, the father was 4 times older than the son. How old is the son, and how old is the father? So, I tried to find a s

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: The father and the son together have 46 years. Three years ago, the father was 4 times older than the son. How old is the son, and how old is the father? So, I tried to find a s      Log On

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Question 824184: The father and the son together have 46 years. Three years ago, the father was 4 times older than the son. How old is the son, and how old is the father?
So, I tried to find a solution.
3 years ago
father 4x
son x
now
father 46-x
son x
4x+3+x+3=46-x+x
5x+6=46 (I omitted the -x and the x)
5x=46-6
5x=40
x=40/5
x=8
So the son is 8 years old and the father is 46-8=38.
Actually, my question is - is my solution right (correct)?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +f+ = father's age now
Let +s+ = son's age now
+f+-+3+ = father's age 3 yrs ago
+s+-+3+ = son's age 3 yrs ago
given:
(1) +s+%2B+f+=+46+
(2) +f+-+3+=+4%2A%28+s+-+3+%29+
----------------------
(2) +f+-+3+=+4s+-+12+
(2) +4s+-+f+=+9+
---------------------
Add (1) and (2)
(1) +s+%2B+f+=+46+
(2) +4s+-+f+=+9+
+5s+=+55+
+s+=+11+
and, since
(1) +s+%2B+f+=+46+
(1) +f+=+46+-+11+
(1) +f+=+35+
The father is 35 and the son is 11
check:
(2) +f+-+3+=+4%2A%28+s+-+3+%29+
(2) +35+-+3+=+4%2A%28+11+-+3+%29+
(2) +32+=+4%2A8+
(2) +32+=+32+
OK