In a survey of students about favorite sports, the results include 20 who like tennis, 24 who like football, 7 who like tennis and football, 14 who like tennis and baseball, 17 who like football and baseball, 3 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?
How many students like only tennis and football?
_ (Type a whole number.)
To find the number of students who like only tennis and football, we need to subtract the students who like tennis, football, and baseball from the students who like both tennis and football.
First, we can find the number of students who like both tennis and football by subtracting the total number of students who like only tennis or only football from the total number of students who like both or all three sports.
Total students who like both or all three sports = 7 (like tennis and football) + 3 (like all three sports) = 10
Total students who like only tennis or only football = Total students who like tennis + Total students who like football - Total students who like both or all three sports
= 20 (like tennis) + 24 (like football) - 10 (like both or all three sports)
= 34 - 10
= 24
Therefore, the number of students who like only tennis and football is 24.
To find the number of students who like only tennis and football, we need to subtract the students who like both tennis and football, as well as the students who like all three sports from the total number of students who like tennis and football.
Given information:
- Number of students who like tennis (Tennis): 20
- Number of students who like football (Football): 24
- Number of students who like both tennis and football (Tennis and Football): 7
- Number of students who like all three sports (Tennis, Football, and Baseball): 3
First, let's calculate the number of students who like only tennis and football.
Step 1: Subtract the number of students who like both tennis and football from the total number of students who like tennis.
Total number of students who like tennis only = Number of students who like tennis - Number of students who like both tennis and football
Total number of students who like tennis only = 20 - 7
Now, let's calculate the result:
Total number of students who like only tennis and football = 13
To find the number of students who like only tennis and football, we need to find the total number of students who like both sports and subtract the students who like all three sports.
According to the given information, 7 students like both tennis and football. However, we need to subtract the 3 students who like all three sports since they are already counted in the category of students who like both tennis and football.
Therefore, the number of students who like only tennis and football can be calculated as follows:
Number of students who like both tennis and football - Number of students who like all three sports
= 7 - 3
= 4
So, there are 4 students who like only tennis and football.