Question

Find the value of the variable and YZ if Y is between X and Z.

XY=4n+3, YZ=2n-7,XZ=22

Answer 1

`\large \boxed{n = (13)/(3); YZ = (5)/(3)}}`

Explanation:

I think you have the situation shown in the diagram below.

1. Calculate the value of n

`\begin{array}{rcl}XY + YZ & = & XZ\\4n+ 3 + 2n - 7 & = & 22\\6n - 4 & = & 22\\6n & = & 26\\n & = & (26)/(6)\\\\& = & \mathbf{(13)/(3)}\\\end{array}\\\large \boxed{\mathbf{n = (13)/(3)}}`

2. Calculate the value of YZ

`\begin{array}{rcl}YZ & = & 2n - 7\\& = & 2\left ((13)/(3)\right ) - 7 \\\\& = & (26)/(3) - 7\\\\& = & (26)/(3) - (21)/(3)\\\\& = & (5)/(3) \\\\\end{array}\\\large \boxed{YZ = \mathbf{ (5)/(3)}}`