Elementary Art School

The music and art department of an elementary art school is attended by 86 students. The music department is attended by 45 students and the art department by 53 students. Some students attend both departments. How many students attend both departments at the same time?

Final Answer:

x =  12

Step-by-step explanation:

$$\begin{gathered} n=86 \\ H=45 \\ V=53 \\ x=H\cap V \\ H=h+x \\ V=v+x \\ h+x+v=n \\ (H-x)+x+(V-x)=n \\ H-x+x+V-x=n \\ x=V+H-n=53+45-86=12 \end{gathered}$$

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