Question

Solve each proportion. If necessary, round to the nearest hundredth.

$\frac{6}{14}=\frac{7}{x-3}$

Short answer

The approximate value is $x\approx 19.33$.

Step-by-step solution

Step 1. Define equivalent ratios.

Equivalent ratios are two ratios that have the same relationship between the numbers.

Step 2. Find the cross products.

The given ratios can be simplified by doing cross product:

$$\begin{gathered} \frac{6}{14}=\frac{7}{x-3} \\ \left(x-3\right)\left(6\right)=\left(7\right)14 \end{gathered}$$

Step 3. Simplify for x.

To further simplify, apply the distributive property to the left-hand side.

$$\begin{gathered} \left(x-3\right)\left(6\right)=\left(7\right)14 \\ 6x-3\left(6\right)=98 \\ 6x-18+18=98+18 \\ \frac{6x}{6}=\frac{116}{6} \end{gathered}$$

Therefore, the approximate value of $x\approx 19.33$.