Question

Use equivalent ratios to solve the proportion.

$\frac{b}{14}=\frac{27}{42}$

Short answer

The solution is $b=9$.

Step-by-step solution

Step 1.  Given

The given proportion is$\frac{b}{14}=\frac{27}{42}.$

Step 2.  To determine

We have to solve the proportion using equivalent ratios.

Step 3.  Calculation 

Solve the given proportion.

$\begin{array}{c}\frac{b}{14\times 3}=\frac{27}{42}\\ \frac{b\times 3}{42}=\frac{27}{42}\left[\text{comparedenominators}\right]\\ \frac{3b}{42}=\frac{27}{42}\left[\text{find}b\right]\\ 3b=27\\ 3b÷3=27÷3\left[\text{divideeachby3}\right]\\ b=9\end{array}$

So, the solution is $b=9$.