Question

Points A,B and C are collinear and B lies between A and C. if AC=48, AB= 2x+2, and BC=3x+6, what is BC?

Answer 1

We know that points A, B and C are collinear, this mean that they are located on the same line. We are given an expression for AB and BC and the measure of AC.

Then we have:

The sum of AB and BC is 48.

`AB+BC=48`

We replace the expression:

`(2x+2)+(3x+6)=48`

Now we solve for x:

`\begin{gathered} 2x+2+3x+6=48 \\ 2x+3x=48-2-6 \\ 5x=40 \\ x=(40)/(5)=8 \end{gathered}`

Now that we have the value of x, we can replace it in the expression for BC.

`\begin{gathered} BC=3x+6 \\ BC=3\cdot8+6 \\ BC=30 \end{gathered}`