Question

Solve the proportion:$\frac{n}{84}=\frac{11}{12}.$

Short answer

The value of n is 77.

Step-by-step solution

Step 1. Given Information

We are given with a proportion having only one variable n and we need to solve the proportion for n:

$\frac{n}{84}=\frac{11}{12}.$

Step 2. Calculating the value of n

In order to solve the proportion we need to multiply both sides of the equation with the LCD of denominators i.e., LCD of 84 and 12 is 84. So,

$$\begin{gathered} \frac{n}{84}=\frac{11}{12}, \\ 84\times \left(\frac{n}{84}\right)=84\times \left(\frac{11}{12}\right), \\ n=7\times 11=77. \\ So,thevalueofnis77. \end{gathered}$$

Step 3. Checking the result

We get the result as 77 now lets check it by putting it in the equation:

$$\begin{gathered} \frac{n}{84}=\frac{11}{12}, \\ \frac{77}{84}=\frac{11}{12}, \\ \frac{11}{12}=\frac{11}{12.} \\ So,ourresultiscorrect. \end{gathered}$$