Answer
$X_{\mathrm{c}\mathrm{m}}=\displaystyle \frac{11}{12}L$
Work Step by Step
Apply equation 9-14 $\qquad X_{\mathrm{c}\mathrm{m}}=\displaystyle \frac{\sum mx}{M}$
$X_{\mathrm{c}\mathrm{m}}=\displaystyle \frac{m_{1}x_{1}+m_{2}x_{2}+m_{3}x_{3}}{m_{1}+m_{2}+m_{3}}$
... all three bricks have the same mass
$=\displaystyle \frac{m(x_{1}+x_{2}+x_{3})}{m+m+m}$
$=\displaystyle \frac{x_{1}+x_{2}+x_{3}}{3}$
The x coordinate of the center of mass of
the first brick is at $L/2$,
the second brick is at $L$,
the third brick is at $L+L/4=5L/4.$
$X_{\mathrm{c}\mathrm{m}}=\displaystyle \frac{\frac{L}{2}+L+\frac{5L}{4}}{3}$
$=\displaystyle \frac{\frac{2L+4L+5L}{4}}{3}$
$=\displaystyle \frac{11}{12}L$
