# Find three consecutive odd integers whose sum is 105

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If the product of two consecutive odd integers is decreased by 3, the result is 12. find the integers

Posted on Sep 21, 2011

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X + ( X + 2 ) + ( X + 4 ) = 105
3X + 6 = 105
3X = 105 - 6
3X = 99
X = 99/3
X = 33
So 33 + 35 + 37 = 105

Posted on Oct 06, 2010

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Let x be the smallest number.
Let x + 2 be the other number (consecutive even integer)

Now to translate the rest;)
three times the smaller 3(x)
19 more -19
sum of the two integers - (x) +( x+2)

Pulling it together,
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collect like terms
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Let X be the lowest of the 3 integers
The sum of the 3 integers can be represented as X + (X+1) + (X+2).
Set this sum equal to 378 and solve for X.
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3X + 3 = 378
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Since X is the lowest of the 3 integers the other 2 will be X+1 and X+2 or 126 and 127.

Therefore, the answer is 125, 126 and 127

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