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

1 Answer
Feb 21, 2016

Answer:

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#