SOLUTION: The positive difference between the squares of two consecutive positive even integers is 52. What is the larger integer?

Question 203192: The positive difference between the squares of two consecutive positive even integers is 52. What is the larger integer?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
How far apart are consecutive even integers? In other words, how much to you add to one even integer to get to the next one? I hope you understand that the answer is two. So if we call out smaller positive even integer "x", then the next one up would be "x+2".

Now that we have expressions for the two consecutive even integers we are in a position to translate "the positive difference between the squares of two consecutive positive even integers is 52"
"The positive difference": Difference means subtraction and a subtraction that works out positive means the first number must be larger than the first.
"the squares of two consecutive positive even integers": and
"The positive difference between the squares of two consecutive positive even integers":
"The positive difference between the squares of two consecutive positive even integers is 52":

Now we have an equation to solve. First we simplify:

This is a simple equation to solve. Subtract 4 from both sides:

Divide both sides by 4:

Since x was the smaller positive even integer, the other one is 2 more or 14.

Checking our work:

Check!

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