Question

Solve the proportion:$\frac{y}{96}=\frac{13}{12}.$

Short answer

The value of y is 104.

Step-by-step solution

Step 1. Given Information

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

$\frac{y}{96}=\frac{13}{12}.$

Step 2. Calculating the value of y

In order to solve the proportion we need to multiply both sides of the equation with the LCD of denominators i.e., LCD of 96 and 12 is 96. So,

$$\begin{gathered} \frac{y}{96}=\frac{13}{12}, \\ 96\times \left(\frac{y}{96}\right)=96\times \left(\frac{13}{12}\right), \\ y=8\times 13=104. \\ So,thevalueofyis104. \end{gathered}$$

Step 3. Checking the result

We get the result as 96 now lets check it by putting it in the equation:

$$\begin{gathered} \frac{y}{96}=\frac{13}{12}, \\ \frac{104}{96}=\frac{13}{12}, \\ \frac{13}{12}=\frac{13}{12}. \\ Hence,ourresultiscorrect. \end{gathered}$$