# Find three consecutive odd integers whose sum is 513

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Posted on Jan 02, 2017

Hi,

Let's say your 3 numbers are a, b and c. Because they are consecutive and odd, you can write them like this:

a = 2x-1, b = 2x+1, c = 2x+3

Now, your problem looks like this:

2(2x-1)(2x+1) = (2x+1)(2x+3) + 7
2(4x^2-1) = 4x^2+6x+2x+3 + 7
8x^2-2 = 4x^2+8x+10
4x^2-8x-12 = 0
4(x^2-2x-3) = 0
x^2-2x-3 = 0

The solutions for this quadratic equation ( see more about this kind of equations here: http://en.wikipedia.org/wiki/Quadratic_equation ) are x=3 or x=-1. So, you've got two sets of solutions:

[1] a = 5, b = 7, c = 9
[2] a = -3, b = -1, c = 1

Take care,
Alex

Posted on Oct 19, 2009

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.
X + (X+1) + (X+2) = 378
3X + 3 = 378
3X = 375
X = 125
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

Posted on Jan 28, 2011

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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