Question

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

$\frac{7}{4}=\frac{f-4}{8}$

Short answer

The value is $f=18$.

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:

$$\begin{gathered} \frac{7}{4}=\frac{f-4}{8} \\ 8\left(7\right)=\left(f-4\right)4 \end{gathered}$$

Step 3. Simplify for f.

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

$$\begin{gathered} 8\left(7\right)=\left(f-4\right)4 \\ 56=4f-4\left(4\right) \\ 56+16=4f-16+16 \\ \frac{72}{4}=\frac{4f}{4} \\ f=18 \end{gathered}$$

Therefore, the value of $f=18$.