SOLUTION: Two numbers differ by 5. Their squares differ by 55. What are the two numbers? Please show me how you get the answer 3 and 8. Thanks!!!

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Question 44261: Two numbers differ by 5. Their squares differ by 55. What are the two numbers?
Please show me how you get the answer 3 and 8. Thanks!!!

Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
Let the two numbers be called "x" and "y".
The numbers differ by 5:
x-y=5.........................(i)
Rearange equation (i) to give x in terms of y:
x=y%2B5.........................(ii)


Their squares differ by 55:
x%5E2-y%5E2=55....................(iii)
Substitute equation (ii) into equation (iii) for x:
%28y%2B5%29%5E2-y%5E2=55
%28y%2B5%29%28y%2B5%29-y%5E2=55
y%5E2%2B10y%2B25-y%5E2=55
10y%2B25=55
10y=30
y=3
substitute "y=3" into equation (ii) to give:
x=3%2B5
So x=8 and y=3
I hope this helps.
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk