SOLUTION: Last year at East High School, a survey showed that 79 students played soccer or basketball, 30 played soccer, and 14 played both. How many of the students played basketbal

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Question 1203879: Last year at East High School, a survey showed that 79 students played soccer or basketball, 30 played soccer, and 14 played both.

How many of the students played basketball?
i know the answer is 63 due to getting the problem incorrect but how would i go ahead and solve this problem?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
students played soccer or basketball,
played soccer, and played both
if so, then played soccer only


since students played soccer or basketball, then played basketball only


so, we have


How many of the students played basketball?
look at set B only




Answer by ikleyn(52780)   (Show Source): You can put this solution on YOUR website!
.

30 played S

14 played both

79 played S or B


For the union of two sets,  S (soccer) and B (basketball), we write

    n(S U B) = n(S) + n(B) - n(S and B)


and substitute there given quantities

      79     = 30   + n(B) - 14.


From this equation, we find the unknown amount

     n(B)    = 79 -30 + 14 = 63.


Thus the answer is: 63 students play basketball.

Solved, with explanations.


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To see many other similar solved problems,  look into the lesson
    - Counting elements in sub-sets of a given finite set
in this site.

Learn the subject  (the basics)  from there.



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