Question #3b198

May 28, 2017

$13$

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

$\left(x - 1\right) - 1 = x - 2$

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

$\left(x - 2\right) + \left(x - 1\right) + x = 36$

This is equivalent to

$3 x - 3 = 36$

Add $3$ to both sides to get

$3 x - \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} + \textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} = 36 + 3$

$3 x = 39$

Finally, divide both sides by $3$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} = \frac{39}{3}$

to get

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{x = 13}}}$