Elementary Art School

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

Correct 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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