SOLUTION: The product of two consecutive odd integers exceed ten times the even number between them by 95. What are the odd integers?

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Question 1197048: The product of two consecutive odd integers exceed ten times the even number between them by 95. What are the odd integers?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39614) About Me  (Show Source):
You can put this solution on YOUR website!
If the odd numbers are n-1 and n+1 then
%28n-1%29%28n%2B1%29=10n%2B95.
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15 and 17

Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.
The product of two consecutive odd integers exceed ten times the even number between them by 95. What are the odd integers?
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Let these two consecutive odd integers be (n-1) and (n+1), where n is the even integer between them.


The problem says  

    (n-1)*(n+1) = 10n + 95.


Simplify and find n

    n^2 - 1 = 10n + 95

    n^2 - 10n - 96 = 0

    (n-16)*(n+6) = 0


The two roots are -6 and 10.


Since the problem allows both positive and negative integer n, we accept both  n= 16  and  n= -6.


ANSWER.   There are two solutions. In one solution odd numbers are 15 and 17.  In other solution odd integers are -7 and -5.

Solved.