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| Math Central | Quandaries & Queries |
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Question from Terry, a student: The product of two consecutive even integers is 14 more than their sum. Find the integers. |
Hi Terry,
Since the smaller of the two integers is even it is divisible by 2 and hence it can be written 2n for some integer n. The next integer 2n + 1 is odd so the next even integer is 2n + 2.
What is the product of 2n and 2n + 2?
What is the sum of 2n and 2n + 2?
What is 14 more than this sum?
This is equal to their product and hence you have an equation you can solve for n.
Penny
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