I am trying to solve this problem
If x+y= 6, y+z= 7 , and x+z= 9 , what is the average of x , y and z ?
Well how i am trying to do is getting the value of 'X' , 'Y' and 'Z' which are X = 4 , Y = 2 , Z = 5 then i take their average as 4+2+5 then 11/3 , but i this is not giving me the right answer. Any help appriciated
$$\begin{align} \underbrace{(x+y)}_{=\,6} + \underbrace{(y+z)}_{=\,7} + \underbrace{(x + z)}_{=\,9} & = 2x + 2y + 2z \\ &= 2(x + y + z) = 6+7+9 \\ &\iff x + y + z =\frac 12(6+7+9)=11\end{align}$$
To compute the average, now, calculate $\dfrac{x + y+z}{3} = \dfrac {11}3$.