Question

Example #5If K is the midpoint of CT, CK = 3x + 23,and KT = 5x + 7, then find x and CT.

Answer 1

Since K is the midpoint of CT, it means that CK is equal to KT,

$CK=KT$

Then, replace with the corresponding expressions,

$3x+23=5x+7$

solve for x,

$\begin{gathered} 3x-5x=7-23 \\ -2x=-16 \\ x=\frac{-16}{-2} \\ x=8 \end{gathered}$

finally, find CT as the addition between CK and KT

$\begin{gathered} CT=CK+KT \\ CT=(3x+23)+(5x+7) \\ x=8 \\ CT=3(8)+23+5(8)+7 \\ CT=24+23+40+7 \\ CT=94 \end{gathered}$

Answer:

$\begin{gathered} 1.\text{ }x=8 \\ 2.\text{ }CT=94 \end{gathered}$