Q38. - Algebra 1

Question

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

$\frac{9b-3}{9}=\frac{5b+5}{3}$

Step-by-Step Solution

Answer

The value is $b=-3$.

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:

 $$\begin{gathered} \frac{9b-3}{9}=\frac{5b+5}{3} \\ 3\left(9b-3\right)=\left(5b+5\right)9 \end{gathered}$$

Step 3. Simplify for b .

To further simplify, apply distributive property on both sides.

 $$\begin{gathered} 3\left(9b-3\right)=\left(5b+5\right)9 \\ 3\left(9b\right)-3\left(3\right)=\left(5b\right)9+\left(5\right)9 \\ 27b-9-45=45b+45-45 \\ 27b-54-27b=45b-27b \\ \frac{-54}{18}=\frac{18b}{18} \\ b=-3 \end{gathered}$$$$\begin{gathered} 3\left(9b-3\right)=\left(5b+5\right)9 \\ 3\left(9b\right)-3\left(3\right)=\left(5b\right)9+\left(5\right)9 \\ 27b-9-45=45b+45-45 \\ 27b-54-27b=45b-27b \\ \frac{-54}{18}=\frac{18b}{18} \\ b=-3 \end{gathered}$$ 

Therefore, the value of $b=-3$.