Question #3b198

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Answer 1 · 2017-05-28T15:09:38

$13$

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

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