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

BC = 30

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

`(5x)/(5)=(40)/(5)`

`x=8`

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

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

Answer 2

`BC=30`

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=(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.