Question

given that B is between A and C, AB=3, BC=4x+1, and AC=16, find x AND BC

Answer 1

We start by drawing the segments:

We can write that AB+BC=AC:

$\begin{gathered} AB+BC=AC \\ 3+(4x+1)=16 \\ 4x+1=16-3 \\ 4x+1=13 \\ 4x=13-1 \\ 4x=12 \\ x=\frac{12}{4} \\ x=3 \end{gathered}$

Then, with thevalue of x, we can calculate BC. But, a simpler way is to use AB+BC=AC:

$\begin{gathered} AB+BC=AC \\ BC=AC-AB=16-3=13 \end{gathered}$

The answers are x=3 and BC=13.