A survey was conducted in a school. It was found that 40% of the students played football,30% played Volleyball and20% played both games.If 90 students played neither football nor volleyed. (1) Draw the above inflation in a Venn-diagram(2) Find the number of students who played football only
150
Since the percentages add to 90%, the 90 students are in the remaining 10%, meaning that there were a total of 900 students.
.4 * 900 = ?
Cannot draw diagrams here.
To draw the Venn diagram, you will need three overlapping circles: one for football, one for volleyball, and one for the intersection of both games. The area outside of the circles represents students who played neither football nor volleyball.
Now let's solve the problem step by step:
1) Start by calculating the number of students who played both football and volleyball. Since 20% of the students played both games, you can find this value by multiplying the total number of students by 0.20:
Number of students who played both games = Total number of students × 0.20
2) Next, calculate the number of students who played only football. Since 40% of the students played football and 20% played both games, you need to subtract the number of students who played both games from the total number of students who played football:
Number of students who played only football = (Total number of students who played football) - (Number of students who played both games)
3) Finally, calculate the number of students who played neither football nor volleyball. It is stated that 90 students played neither game, so this value should be equal to the complement of all students who played any of the games:
Number of students who played neither game = Total number of students - [(Number of students who played football) + (Number of students who played volleyball) - (Number of students who played both games)]
Now, substitute the given information into the formulas above to find the number of students who played football only.