```Question 164600
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 ```