Question

Point C is between A and B on AB. Use the given information to write an equation in terms of x. Then solve the equation to find x, AC, BC, and AB.

Answer 1

We have the following:

$\begin{gathered} AB=AC+CB \\ AC=2x+5 \\ AB=27x \\ CB=5x+15 \end{gathered}$

replacing:

$\begin{gathered} 27x=2x+5+5x+15 \\ 27x-2x-5x=20 \\ 20x=20 \\ x=\frac{20}{20} \\ x=1 \end{gathered}$

Therefore:

$\begin{gathered} AC=2\cdot1+5=7 \\ AB=27\cdot1=27 \\ CB=5\cdot1+15=20 \end{gathered}$

x = 1

AC = 7

AB = 27

CB = 20