SOLUTION: 42: The difference between the square of one even number and the square of the next smaller even number is 52. What is the larger number?

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Question 80744: 42: The difference between the square of one even number and the square of the next smaller even number is 52. What is the larger number?
Found 2 solutions by dolly, stanbon:
Answer by dolly(163) About Me  (Show Source):
You can put this solution on YOUR website!
Let one even number be x
so the next even number = x+2
So (x+2)^2 - x^2 = 52
==> x^2 + 4x + 4 - x^2 = 52
==> 4x + 4 = 52
==> 4x = 52 - 4
==> 4x = 48
==> x = 48/4
==> x = 12
So the larger even number = x+2
= 14

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between the square of one even number and the square of the next smaller even number is 52. What is the larger number ?
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Let the larger even number be 2(n+1)
Let the smaller even number be 2n
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EQUATION:
(2n+2)^2 - (2n)^2 = 52
(2n)^2+8n+4 - (2n)^2 = 52
8n+4 = 52
8n=48
n=6
2n=12 (the smaller even number)
2n+2=14 (the larger even number)
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Cheers,
Stan H.