Find Three Consecutive Odd Integers

Find three consecutive odd integers whose sum is 117.

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Odd integers, such as 1,3,5,7,...... increase by 2 each time.  
Therefore, if the first is x, then:

x = 1st consecutive odd integer
x + 2 = 2nd consecutive odd integer
x + 4 = 3rd consecutive odd integer

x + x + 2 + x + 4 = 117   {their sum is 117}
3x + 6 = 117   {combined like terms}
3x = 111   {subtracted 6 from each side}
x = 37   {divided each side by 3}

Remember, x is the first odd integer.

x + 2 = 39   {substituted 37, in for x, into x + 2}
x + 4 = 41   {substituted 37, in for x, into x + 4}

37, 39, and 41 are the three consecutive odd integers

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