SOLUTION: One number is 3 more than another. The difference between their squares is 51. What are the numbers?

Question 1008696: One number is 3 more than another. The difference between their squares is 51. What are the numbers?
Found 2 solutions by stanbon, fractalier:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One number is 3 more than another. The difference between their squares is 51. What are the numbers?
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Equations:
x = y + 3
x^2 - y^2 = 51
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Substitute for "x" and solve for "y"::
(y+3)^2 - y^2 = 51
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y^2+6y+9 - y^2 = 51
6y+9 = 51
6y = 60
y = 10
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solve for "x"::
x = y + 3
x = 13
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Cheers,
Stan H.
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Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the numbers x and y. Thus we have
x = y + 3 and
x^2 - y^2 = 51
Now substitute and get
(y+3)^2 - y^2 = 51
y^2 + 6y + 9 - y^2 = 51
6y + 9 = 51
6y = 42
y = 7
x = 10

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