There are a $100$ students, $50$ do not play sports, $70$ do not play music and $40$ play neither sports nor music. How many students play sports and music. Explain your answer
My attempt so far was two sets (No sports and no music) and outside was no music or sport
The answers that I have gotten are either $10$ or $20$ to get $10$ I have added $50 + 70 - |A \cap B| + 40$ then take $100$ away from that
To get 20 I have done $50 + 70 = 120$ Then I did $120 - 100 = 20$
My question is how would I find $|A \cap B|$
Edit -
I have been looking at different ways and have found that the answer could be $60$
This is due to adding $50 + 40 + 70 = 160$
From there I take $160 - 100 = 60 $
The answer is $20$
The $70$ who do not play music comprise the $40$ who do neither and therefore $30$ who do sport only.
Likewise, the 50 who do not play sport comprise the 40 who do neither and therefore $10$ who only play music.
That leaves $20$ to make the total up to $100$ and these play both music and sport.