Question

94 cities were surveyed to determine sports teams. 26 had baseball, 23 had football, 22 had basketball, 12 baseball and football, 13 had baseball and basketball, 14 had football and basketball, and 7 had all three.A) How many had only a basketball team?B) How many had baseball or football?C) How may had baseball or football, but not basketball?

Answer 1

A) 2

B) 33

C) 13

Explanation:

Baseball =26

Football = 23

Basketball = 22

Baseball and Football (BF) = 12

Baseball and basketball (BK) = 13

Football and basketball (FK) = 14

All three (BFK) = 7

A) The total number of cities that have basketball teams is given by the cities with basketball only, added to the cities with basketball and football and cities with basketball and baseball, minus the cities with all three sports:

`22=K+BK+FK-BFK\\22=K+13+14-7\\K=2`

B) The total number of cities with baseball of football is given by sum of the cities with either sport, minus the number of cities with both sports:

`B\ or\ F = 23+22-12\\B\ or\ F =33`

C) If 22 cities have basketball and only 2 have basketball only, 20 cities have basketball and either baseball, football or all three sports. The number of cities with baseball or football, but not basketball is:

`(B\ or\ F)\cap (not\ K) = 33-20=13`