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

Answer:

BC = 30

Step-by-step explanation:

Look at the picture.

The equation:

$(2x+2)+(3x+6)=48$        combine like terms

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

$5x+8=48$         subtract 8 from both sides

$5x+8-8=48-8$

$5x=40$           divide both sides by 5

$\dfrac{5x}{5}=\dfrac{40}{5}$

$x=8$

$BC=3x+6$ - put x = 8:

$BC=3(8)+6=24+6=30$

Answer 2

Answer:

$BC=30$

Step-by-step explanation:

Given: Points A, B, and C are collinear. B lies between A and C. $\text{AC}=48$ , $\text{AB}=2x+2$, and $\text{BC}=3x+6$

To find: BC

Solution: It is given that Points A, B, and C are collinear. As B is between A and C. So, we have

$AB+BC=AC$

Here, $\text{AC}=48$ , $\text{AB}=2x+2$, and $\text{BC}=3x+6$

So, $2x+2+3x+6=48$

$\implies5x+8=48$

$\implies 5x=48-8$

$\implies 5x=40$

$\implies x=\frac{40}{5}$

$\implies x=8$

Now, BC is $3x+6$

On putting $x=8$ in $3x+6$

$BC=3(8)+6$

$BC=24+6$

$BC=30$

Hence, BC is 30.