In a survey of students about favorite sports, the results include 23 who like tennis,30 who like football, 7 who like tennis and football,19 who like tennis and baseball, 22 who like football and baseball, 4 who like all three sports, and 7 who like none of the sports. How many students like only tennis and football? How many students like only tennis and baseball? How many students like only baseball and football?
Let's solve this using a Venn diagram.
First, let's fill in the number of students who like each sport: Tennis = 23, Football = 30, Baseball = unknown.
Next, let's fill in the overlapping regions: Tennis & Football = 7, Tennis & Baseball = 19, Football & Baseball = 22, All three = 4.
Lastly, let's fill in the students who like none of the sports = 7.
Now, let's find the number of students who like only each combination.
Number of students who like only Tennis and Football = Tennis & Football - All three = 7 - 4 = 3.
Number of students who like only Tennis and Baseball = Tennis & Baseball - All three = 19 - 4 = 15.
Number of students who like only Baseball and Football = Football & Baseball - All three = 22 - 4 = 18.
To determine how many students like only tennis and football, we need to subtract the number of students who like tennis and football from the total number of students who like tennis.
Total number of students who like tennis = 23
Number of students who like tennis and football = 7
Therefore, the number of students who like only tennis and football = 23 - 7 = 16.
To determine how many students like only tennis and baseball, we need to subtract the number of students who like tennis and baseball from the total number of students who like tennis.
Number of students who like tennis and baseball = 19
Therefore, the number of students who like only tennis and baseball = 23 - 19 = 4.
To determine how many students like only baseball and football, we need to subtract the number of students who like baseball and football from the total number of students who like football.
Total number of students who like football = 30
Number of students who like football and baseball = 22
Therefore, the number of students who like only baseball and football = 30 - 22 = 8.
To find the number of students who like only tennis and football, we need to subtract the number of students who like both tennis and football from the total number of students who like football.
First, let's calculate the number of students who like both tennis and football:
Number of students who like tennis and football = 7
Next, let's calculate the number of students who like only football:
Number of students who like only football = Number of students who like football - Number of students who like both tennis and football
= 30 - 7
= 23
Therefore, 23 students like only football.
Now, let's calculate the number of students who like only tennis and baseball.
Number of students who like only tennis and baseball = Number of students who like tennis and baseball - Number of students who like all three sports
= 19 - 4
= 15
Therefore, 15 students like only tennis and baseball.
Finally, let's calculate the number of students who like only baseball and football.
Number of students who like only baseball and football = Number of students who like baseball and football - Number of students who like all three sports
= 22 - 4
= 18
Therefore, 18 students like only baseball and football.