Question

How do you find three consecutive odd integers that have a sum of 123?

Answer 1

Hint: We will first assume the three odd integers and then sum them up and put it equal to 123. Now, we will get one integer and thus get the rest.

Complete step-by-step answer:
Let the first odd integer be x.
Now, the first odd integer is x, the next is x + 2 and thus the last will be x + 4.
Now, since the sum of them all is given to be 123.
So, we will get: x + (x + 2) + (x + 4) = 123
If we open up the bracket, we will get the following equation:-
$ \Rightarrow $x + x + 2 + x + 4 = 123
If we club all the x’s on the left hand side, we will then obtain the following equation:-
$ \Rightarrow $3x + 2 + 4 = 123
Now if we add up the constants on the left hand side, we will get:-
$ \Rightarrow $3x + 6 = 123
Taking the 6 from addition in the left hand side to subtraction in right hand side, we will then obtain the following equation:-
$ \Rightarrow $3x = 123 – 6
Now, if we do the simplification on the right hand side, we will then obtain:-
$ \Rightarrow $3x = 117
Dividing both sides by 3, we will then obtain:-
$ \Rightarrow $x = 39

Thus, the consecutive odd integers are 39, 41 and 43.

Note:
The students must note that if we would have consecutive integers, we would have taken x, x + 1 and x + 2 but here we have consecutive odd integers, therefore, we skipped the even from in between. So, when we took the first integer to be x. Now, the next integer will be x + 1 but it will be even. Now, the next integer which is (x + 2) will be odd. Thus , we move forward.