Question

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

Answer 1

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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`color(blue)("The seed value is "n)`

Let any even number be `2n`

Then any odd number is `2n+1`

If the first odd number be `2n+1`
Then the second odd number is `" "2n+1+2" "=" "2n+3`

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

Next number is even: `" "(2n+1)+1=2n+2`

Next number is odd:`" "(2n+2)+1=2n+3`

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Using the above notation

Let the first odd number be:`" "2n+1`
Let the second odd number be:`" "2n+3`

Given that: `" "(2n+1) +(2n+3)=56`

`=> 4n+4=56`

`=> n=52/4=13`

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so the first odd number:`" "2n+1=2(13)+1" "=" "27`

second odd number is `27+2=29`

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Check:

`29+27=56`