# Given a set  {12, x ,17} , for what x would the mean be 14?

Dec 7, 2015

$x = 13$

#### Explanation:

$\textcolor{w h i t e}{\times} \overline{a} = \frac{1}{n} {\sum}_{i = 1}^{n} {a}_{i}$ (the mean of a set of n data points)

$\textcolor{w h i t e}{\times} 14 = \frac{1}{3} {\sum}_{i = 1}^{3} {a}_{i}$
$\implies \frac{12 + x + 17}{3} = 14$

Multiply both sides by $3$
$\textcolor{w h i t e}{\times} \textcolor{red}{3 \cdot} \frac{12 + x + 17}{3} = \textcolor{red}{3 \cdot} 14$
$\implies x + 29 = 42$

Add $- 29$ to both sides
$\textcolor{w h i t e}{\times} x + 29 \textcolor{red}{- 29} = 42 \textcolor{red}{- 29}$
$\implies x = 13$