Question

Solve:$\frac{v+30}{8}=\frac{v+66}{12}.$

Short answer

The value of v is 42.

Step-by-step solution

Step 1. Given Information

We are given with two ratios equal to each other and we need to solve it for x:

$\frac{v+30}{8}=\frac{v+66}{12}.$

Step 2. Solving for x

Firstly find LCM of 8 and 12 which is 24

Now, multiply both sides of the equation with this LCM and solving for x:

$$\begin{gathered} \frac{v+30}{8}=\frac{v+66}{12}, \\ 24\times \left(\frac{v+30}{8}\right)=24\times \left(\frac{v+66}{12}\right), \\ 3\times (v+30)=2\times (v+66). \\ 3v+90=2v+132, \\ v=132-90=42. \end{gathered}$$

So,$v=42isourfinalresult.$

Step 3. Checking the result

We get $v=42$as our result and now we will check it from the original equation:

$$\begin{gathered} Putv=42in: \\ \frac{v+30}{8}=\frac{v+66}{12}, \\ \frac{42+30}{8}=\frac{42+66}{12}, \\ \frac{72}{8}=\frac{108}{12}, \\ 9=9. \\ Hence,ourresultiscorrect. \end{gathered}$$