B. Solve the following:
1. In a class of 35 students, 22 are studying Korean, 15 are studying Chinese, and 9
are studying both Korean and Chinese. How many students are not studying any
foreign language?
opt
2. Out of 40 athletes, 21 play basketball, 19 play volleyball, 13 play soccer, 10 play
basketball and volleyball, 8 play basketball and soccer, 4 play volleyball and
soccer, and 2 play the three sports. How many athletes do not play any of the three
sports?
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Answer:
1.) 7
2.)7
Step-by-step explanation:
1.)There are a total of 35 students, in the class. Out of these 22 students are studying Korean while 15 students are studying Chinese. Interestingly there are 9 students who have chosen to study both Korean and Chinese.
Now lets calculate the number of students who are studying one foreign language. By adding the number of students studying Korean and Chinese (22 + 15) and then subtracting the overlap (9) we find that a total of 28 students are studying one foreign language.
On the hand we have some students who have not opted to study any language. By subtracting the number of students studying one foreign language (28) from the total number of students (35) we can conclude that there are precisely 7 students who have decided not to study any foreign language.
In summary there are indeed 7 students, in our class who have not chosen to study any language.
2.) Out of the 40 athletes 21 of them play basketball while 19 play volleyball and 13 play soccer. Among them there are 10 who play both basketball and volleyball 8 who participate in both basketball and soccer and 4 who are involved in both volleyball and soccer. Additionally there are 2 athletes who actively participate in all three sports.
To determine the number of athletes not engaged in any of these sports we subtract the number of athletes involved, in least one sport, from the overall count;
Total number of athletes engaged in at least one sport = (21 + 19 + 13). (10 + 8 + 4) + 2 =33.
Therefore we can conclude that there are a total of 7 athletes who do not participate in any of these three sports out of the count of 40.