SOLUTION: two integers differ by four while their squares differ by 200. What is the product of the two integers?

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: two integers differ by four while their squares differ by 200. What is the product of the two integers?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 891518: two integers differ by four while their squares differ by 200. What is the product of the two integers?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A=B%2B4
1.A-B=4
.
.
2.A%5E2-B%5E2=200
This is a difference in squares you can simplify.
%28A-B%29%28A%2BB%29=200
Substituting from eq. 1,
4%28A%2BB%29=200
3.A%2BB=50
So then adding eq. 1 and eq. 3,
A-B%2BA%2BB=4%2B50
2A=54
A=27
Then from eq. 1,
27=B%2B4
B=23