Q33. - Algebra 2

Question

If $\frac{\mathbf{a}}{\mathbf{b}}\mathbf{=}\mathbf{8}$ and $\mathbf{ac}\mathbf{-}\mathbf{5}\mathbf{=}\mathbf{11}$, then $\mathbf{bc}\mathbf{=}$

A.93        B. 2      C. $\frac{\mathbf{5}}{\mathbf{8}}$     D. cannot be determined

Step-by-Step Solution

Answer

The value of $bc$ is 2.

Step 1 – Description of step.

Add 5 on both the sides of $ac-5=11$ and simplify.

$\begin{array}{c}ac-5+5=11+5\\ ac=16\\ c=\frac{16}{a}\end{array}$

Step 2 – Description of step.

Divide each side of the $\frac{a}{b}=8$ and simplify.

$\begin{array}{c}\frac{\frac{a}{b}}{a}=\frac{8}{a}\\ \frac{1}{b}=\frac{8}{a}\\ b=\frac{a}{8}\end{array}$

Step 3 – Description of step.

Substitute $\frac{16}{a}$ for c and $\frac{a}{8}$ for b into $bc$ and simplify.

$\begin{array}{c}bc=\frac{a}{8}\cdot \frac{16}{a}\\ =\frac{16}{8}\\ =2\end{array}$

The value of $bc$ is 2. Therefore, option B is the correct answer.