SOLUTION: Paul is 3 years younger than his friend Peter. In seven years, the product of their ages will be five more than the product of their ages five years ago. How old are they now?

Question 164598: Paul is 3 years younger than his friend Peter. In seven years, the product of their ages will be five more than the product of their ages five years ago. How old are they now?
Answer by MRperkins(300) (Show Source): You can put this solution on YOUR website!
Paul is 3 years younger than his friend Peter.
so:
Let Peter=x and Paul=x-3
In seven years, the product of their ages will be five more than the product of their ages five years ago.
So:
Peter's age (x) in seven years will be (x+7) and Paul's age in seven years will be [(x-3)+7].
The product of their ages at that time will be[(x+7)*(x-3+7)].
Peter's age (x) five years ago was (x-5) and Paul's age five years ago was (x-3-5).
The product of their ages at that time will be[(x-5)*(x-3-5)].
The product of their ages in seven years is 5 more than it was five years ago.
Therefore:
[x+7)(x-3+7)=(x-5)(x-3-5)+5
simplify:
[x+7)(x+4)=(x-5)(x-8)+5
FOIL
x^2+4x+7x+28=x^2-8x-5x+40+5
combine like terms
x^2+11x+28=x^2-13x+45
subtract x^2 from both sides
11x+28=-13x+45
add 13x to both sides
24x+28=45
Subtract 28 from both sides
24x=17
divide both sides by 24
x=17/24 years old
since Peter=x, Peter is 17/24 years old; however this doesn't make much since. So to convert to months, we will set 17/24 equal to x/12 and solve for x

cross multiply and 17*12=24x or 204=24x
divide both sides by 24 and get x=8.5
Therefore Peter is 8.5 months old and Paul will be born in 27.5 months
I hope this helps

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