Question

Question #3b198

Answer 1

`13`

Explanation:

As an alternative approach, you can start by saying that `x` is the largest number in the sequence.

In this case, the number that comes before `x` would be equal to `x -1`.

Similarly, the number that comes before the number that comes before `x` would be

`(x-1) - 1 = x - 2`

You know that the sum of the three consecutive integers is equal to `36`, so you can say that

`(x-2) + (x-1) + x = 36`

This is equivalent to

`3x - 3 = 36`

Add `3` to both sides to get

`3x - color(red)(cancel(color(black)(3))) + color(red)(cancel(color(black)(3))) = 36 + 3`

`3x = 39`

Finally, divide both sides by `3`

`(color(red)(cancel(color(black)(3)))x)/color(red)(cancel(color(black)(3))) = 39/3`

to get

`color(darkgreen)(ul(color(black)(x = 13)))`