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

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Question 254303: The product of two consecutive odd integers exceeds ten times the even number between them by 95. What are the two odd integers?
Found 3 solutions by drk, JimboP1977, palanisamy:
Answer by drk(1908)   (Show Source):
You can put this solution on YOUR website!
Let 2 consecutive odd integers be x and x + 2.
Let the even number between then be x + 1.

x = 15 or x = -7.
We have two answers:
15, 17
-7, -5.
Now the question could be "could x be negative?" Let's see,we can try our answers on the original question of "The product of two consecutive odd integers exceeds ten times the even number between them by 95"
(-7)*(-5) - 10*(-6) = 95
35 + 60 = 95
95 = 95.
So we see that negatives do work.

Answer by JimboP1977(311)   (Show Source):
You can put this solution on YOUR website!
x*(x+2)=10*(x+1)+95
x^2+2x=10x+10+95
x^2+2x=10x+105
x^2-8x=105
(x-4)^2-16=105
(x-4)^2=121
x=sqrt(121)+4
x=15
So the two odd integers are 15 and 17.

Answer by palanisamy(496)   (Show Source):
You can put this solution on YOUR website!
Let the two consecutive odd integers be x and x+2
The even integer between them is x+1
Given,the product of two consecutive odd integers exceeds ten times the even number between them by 95
x(x+2) = 10(x+1)+95
x^2+2x = 10x+10+95
x^2+2x-10x-10-95 = 0
x^2-8x-105 = 0
(x-15)(x+7) = 0
x = 15 or -7
X cannot be negative.
Therefore x = 15.
So the odd integers are 15 and 17