# The sum of two consecutive odd integers is 56, how do you find the two odd integers?

Feb 21, 2016

The odd numbers are 29 and 27

#### Explanation:

There are several way to do this. I am opting to use the derivation of odd number method. The thing about this is that is uses what I call a seed value that has to be converted to arrive at the value you want.

If a number is divisible by 2 yielding an integer answer then you have an even number. To convert this to odd just add or subtract 1
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$\textcolor{b l u e}{\text{The seed value is } n}$

Let any even number be $2 n$

Then any odd number is $2 n + 1$

If the first odd number be $2 n + 1$
Then the second odd number is $\text{ "2n+1+2" "=" } 2 n + 3$

Think like this: 1^("st") "odd is "2n+1

Next number is even: $\text{ } \left(2 n + 1\right) + 1 = 2 n + 2$

Next number is odd:$\text{ } \left(2 n + 2\right) + 1 = 2 n + 3$

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Using the above notation

Let the first odd number be:$\text{ } 2 n + 1$
Let the second odd number be:$\text{ } 2 n + 3$

Given that: $\text{ } \left(2 n + 1\right) + \left(2 n + 3\right) = 56$

$\implies 4 n + 4 = 56$

$\implies n = \frac{52}{4} = 13$

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so the first odd number:$\text{ "2n+1=2(13)+1" "=" } 27$

second odd number is $27 + 2 = 29$

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Check:

$29 + 27 = 56$