45% liked literature, 70% liked music and 15% liked none.if 60 students liked both subjects. Find the number of students participated in this survey.
Use a VENN diagram here.
15% like none
45% - overlap like literature
70% - overlap like music
These are supposed to add up to 100%
The add up to 130 which means that 30% would be in the overlap of liking both
.30 x = 60
x = 200
x = 400
200
To find the total number of students who participated in the survey, we need to consider the percentages of students who liked literature and music and those who liked neither.
Let's start with the percentage of students who liked literature. According to the given information, 45% liked literature.
Similarly, the percentage of students who liked music is given as 70%.
Next, we know that 15% liked none of the subjects.
To find the number of students who liked literature only, we subtract the percentage of students who liked both subjects (60 students) from the percentage who liked literature. So the number of students who liked literature only is 45% - 60 = 45% - 0.45 * 60.
To find the number of students who liked music only, we subtract the percentage of students who liked both subjects (60 students) from the percentage who liked music. So the number of students who liked music only is 70% - 60 = 70% - 0.70 * 60.
Now, to find the number of students who participated in the survey, we need to add together the number of students who liked literature only, the number of students who liked music only, the number of students who liked both subjects, and the number of students who liked neither.
Let's calculate:
Number of students who liked literature only = 45% - 0.45 * 60
Number of students who liked music only = 70% - 0.70 * 60
Number of students who liked both subjects = 60
Number of students who liked neither = 15%
Finally, to find the total number of students who participated in the survey, we add the numbers we calculated above:
Total number of students = Number of students who liked literature only + Number of students who liked music only + Number of students who liked both subjects + Number of students who liked neither
To find the number of students who participated in the survey, we can first find the total number of students who liked literature and music separately.
Let's assume the total number of students who participated in the survey is "x".
From the given information, we know that 45% of the students liked literature and 70% liked music. Since 15% of the students liked neither, we can subtract this percentage from 100% to find the percentage of students who liked either literature or music.
Percentage of students who liked either literature or music = 100% - 15% = 85%
Now, we can calculate the number of students who liked literature and music separately.
Number of students who liked literature = (45% of x) / 100 = 0.45x
Number of students who liked music = (70% of x) / 100 = 0.7x
We also know that 60 students liked both literature and music.
So, the total number of students who liked either literature or music can be calculated using the formula:
Total number of students who liked either literature or music = Number of students who liked literature + Number of students who liked music - Number of students who liked both
Total number of students who liked either literature or music = 0.45x + 0.7x - 60
Since the percentage of students who liked either literature or music is 85%, we can set up the equation:
(0.45x + 0.7x - 60) / x = 85/100 = 0.85
To solve for x, we can multiply both sides of the equation by x:
0.45x + 0.7x - 60 = 0.85x
Combining like terms:
1.15x - 60 = 0.85x
Subtracting 0.85x from both sides:
0.3x - 60 = 0
Adding 60 to both sides:
0.3x = 60
Dividing both sides by 0.3:
x = 60 / 0.3
x = 200
Therefore, 200 students participated in this survey.