SOLUTION: A dad is now three times as old as his son, but in eleven years the dad will be only two times as old as his son is then. How old will the dad be next year?

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Question 316442: A dad is now three times as old as his son, but in eleven years the dad will be only two times as old as his son is then. How old will the dad be next year?
Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
Dad is three times as old as Son. Written as an equation this says D+=+3+%2A+S (eq1)
In 11 years, Dad's age will be D+11. Son's age will be S+11. At that time, Dad will be only 2 times as old as Son, so %28D%2B11%29+=+2%2A%28S%2B11%29. (eq2)
Let's plug in the expression for D given by (eq1) into (eq2).
%28D%2B11%29+=+2%2A%28S%2B11%29
%283%2AS%2B11%29+=+2%2A%28S%2B11%29
Now distribute the 2 on the right hand side to get
3S%2B11+=+2S%2B22%29
Subtract 11 from both sides to get
3S+=+2S%2B11%29
Subtract 2S from both sides to get +S+=+11.
If the Son is 11, the Dad who is three times as old must be 33. Next year Dad will be 34.
Now we check. In 11 years, Son will be 22 and Dad will be 44. Indeed, Dad's age is two times the age of the son, so this answer checks.