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Fifty students were surveyed about their participation in hockey and baseball. The results of the survey were:

 33 students played hockey

24  students played baseball

8  students played neither hockey nor baseball

How many of the students surveyed played both hockey and baseball?

 Jan 6, 2019
 #1
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15 play both

 Jan 6, 2019
 #2
avatar+595 
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We know \(50-8=42\) students played at least one sport. Now, we see that \(33+24=57\), but there couldn't be 57 players with only 42 students! Therefore, some play both. In fact, \(57-42=15\) students played both.

 

You are very welcome!

:P

 Jan 6, 2019
 #3
avatar+17331 
+3

I suspect you may have wanted a Venn Diagram for this:

 

 Jan 6, 2019
 #4
avatar+3994 
+2

We can set up an equation: \((33-x)+(24-x)+x+8=50\) . Solving, we get \(57-x+8=50, 57-x=42\)\(\) , so   \(\boxed{x=15}.\)

.
 Jan 6, 2019

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