Question

Three collinear points $A,B$ and $C$ ares such that point $B$ is between points $A$ and $C$. The distance from $A$ to $B$ is $8$ more than $4$ times the distance from $B$ to $C$ and the distance from $A$ to $C$ is $5$ times the distance from $B$ to $C$. What is the distance from $A$ to $C$?

• A. $4$
• B. $20$
• C. $16$
• D. $24$

Answer 1

The correct option is B $20$

From "length of segment $AC$ is $5$ times the length of segment of $BC$" it is clear that $AC$ is the longer part.

So call the endpoints of your line $A$ and $C$ and place $B$ between them.

Let $BC=x$

Then $AC=5x$ and $AB=4x$
Then it is given that, " the distance from point $A$ to point $B$ is $8$ more than twice the distance from point $B$ to point $C$ "

$\Rightarrow AB=2\left(BC\right)+8$
$\Rightarrow 4x=2x+8$
$\Rightarrow 2x=8$
$\Rightarrow x=4$
Then $AC=5x=20$.

Hence, the distance from $A$ to $C$ is $20$.