# The sum of two consecutive integers is 68, what is the smaller number?

##### 1 Answer

#### Explanation:

Two consecutive number means that one of them is even and the other odd. Consequently their sum will be odd.

For the sum to be 68 the question has to be one of:

Two consecutive even numbers give an even number answer.

Two consecutive odd numbers give an even number answer.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let

Then

So

Thus

So

Subtract 2 from both sides

Thus the 1st even number is

Thus the next even number is

.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using the notation from the first solution

If

The second odd number will be

So

Divide both sides by 4

So the first odd number is

So the second odd number is