In an examination 70 student failled in math¡A90failed in science and 20 failed in both. if 80 student passed in math using venn-daigram¡A find how mamy student were passed in both subject¡H
To find the number of students who passed in both subjects, we need to subtract the number of students who failed in both subjects from the total number of students who passed in math.
Let's denote the number of students who passed in both subjects as "x".
From the given information:
- The number of students who failed in math = 70
- The number of students who failed in science = 90
- The number of students who failed in both subjects = 20
Let's represent this information in a Venn diagram:
/\
/ \
Math (-) | x | |
\ /
\/
|
Science (-) | |
|
/\
/ \
Both (-) | 20 |
\ /
\/
Using the formula for finding the number of elements in the union of two sets, we can write:
Total number of students = Number of students who passed in math + Number of students who failed in math
= 80 + 70 = 150
Similarly for science, we have:
Total number of students = Number of students who passed in science + Number of students who failed in science
= Number of students who passed in both subjects + Number of students who failed in both subjects + Number of students who passed in science only
= x + 20 + 90 = x + 110
Since the total number of students remains the same, we can equate the equations:
150 = x + 110
Solving for x:
x = 150 - 110
x = 40
Therefore, 40 students passed in both subjects.
To find the number of students who passed in both subjects, we need to use the information given and the concept of Venn diagrams.
Let's break down the information given:
- 70 students failed in math.
- 90 students failed in science.
- 20 students failed in both subjects.
- 80 students passed in math.
We can represent this using a Venn diagram. Draw two overlapping circles to represent math and science, and label the parts as shown below:
_______
/ /
/ /
/ M /
/______/
_______
/ /
/ S /
/______/
Now, let's fill in the given information on the Venn diagram:
- 70 students failed in math, so put 70 outside the circle labeled "M".
- 90 students failed in science, so put 90 outside the circle labeled "S".
- 20 students failed in both subjects, so put 20 in the overlapping region of the circles.
We are given that 80 students passed in math. To find out how many students passed in both subjects, we need to subtract the number of students who only passed math from this total.
Since the total number of students who passed math is 80 and the number of students who failed in math is 70, we can calculate the number of students who only passed math as:
Only passed math = Total passed math - Failed math
Only passed math = 80 - 70 = 10
Therefore, out of the 80 students who passed math, 10 of them only passed math, leaving us with:
Passed in both subjects = Total passed math - Only passed math
Passed in both subjects = 80 - 10 = 70
So, there are 70 students who passed in both subjects (math and science).