The mean of $7, 9, x + 3, 12, 2 x - 1,$ and $3$ is $9 .$ Find the value of $x .$

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Solution

Given
The numbers are $= 7, 9, x + 3, 12, 2 x - 1, 3$
Total numbers $= 6$
Sum of the given numbers $= 7 + 9 + x + 3 + 12 + 2 x - 1 + 3$
$= 3 x + 33$
the mean of numbers $= 9$
Therefore,
Required mean $= \frac{3 x + 33}{6}$
$\begin{array}{rcl} \Rightarrow & 9 = \frac{3 x + 33}{6} \\ \Rightarrow & 9 \times 6 = 3 x + 33 \\ \Rightarrow & 54 = 3 x + 33 \\ \Rightarrow & 54 - 33 = 3 x \\ \Rightarrow & 21 = 3 x \\ \Rightarrow & x = \frac{21}{3} \\ \Rightarrow & x = 7 \end{array}$
Hence, the value of $x$ is $7$

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