in the diagram, point y is the midpoint of seg. XZ, XY=3a +1, & YZ=a+9 for some constant, a. find the length of segment XZ

In the diagram, point Y is the midpoint of seg. XZ, XY = 3a +1, & YZ = a+9 for some constant, a. find the length of segment XZ.

If Y is the midpoint of XZ, then XY=YZ

$\begin{array}{|rcll|} \hline XY &=& YZ \\ 3a +1 &=& a+9 \\ 2a &=& 8 \\ \mathbf{a} &=& \mathbf{4} \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline XZ &=& XY +YZ \\ XZ &=& (3a +1) + (a+9) \\ XZ &=& 4a+10 \quad | \quad a=4 \\ XZ &=& 4\cdot 4 + 10 \\ XZ &=& 16+10 \\ \mathbf{XZ} &=& \mathbf{26} \\ \hline \end{array}$