SOLUTION: a man is 5times as old as his son. In 5 years he will be only 3 times as old as his son, find the present age?

Question 281515: a man is 5times as old as his son. In 5 years he will be only 3 times as old as his son, find the present age?
Found 2 solutions by Mathematicians, JBarnum:
Answer by Mathematicians(84) (Show Source): You can put this solution on YOUR website!
These word problems are always tricky, basically you want to set up two equations in order to find both their ages.
From the first sentence, "a man is 5 times as old as his son"
I will let X be the age of the old guy and Y be the age of his son:

You can test that this equation is right, if his son was 1 years old, then the man would be 5 which is 5 times more then 1!
Continuing on with the second sentence
In 5 years he will be only 3 times as old as his son, find the present age?
If 5 years progress, both him and his son will have to add 5 years so:

To solve this equation, we know that so we plug in 5Y for every X.
becomes
Using distribution
Subtract 3Y on both sides and 5 on both sides
Finally divide both sides by 2

Which says his son is 5 years old, how old is the man?
Go back to any equation, this will be easiest with this one:

The man is 25 and his son is 5.

Answer by JBarnum(2146) (Show Source): You can put this solution on YOUR website!
=mans present age
=sons present age
"a man is 5times as old as his son."
"In 5 years he will be only 3 times as old as his son" "In 5 years" means man+5 years and son+5 years
use substitution for m and solve for s

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