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?
bc =

Explanation:

Step1: Set up total length equation

Since $A, B, C$ are collinear with $B$ between $A$ and $C$, $AB + BC = AC$. Substitute the given values:
$$(2x + 2) + (3x + 6) = 48$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$5x + 8 = 48$$
$$5x = 48 - 8 = 40$$
$$x = \frac{40}{5} = 8$$

Step3: Calculate $BC$

Substitute $x=8$ into $BC = 3x + 6$:
$$BC = 3(8) + 6$$

Answer:

30