in a class of 300 students,they were given mathematics test in three subjects namely,economics,statistics and mathematics,90 students failed in economics,100 failed in statistics,96 failed in mathematics,60 failed in economics and statistics,64 failed in statistics and mathematics,70 failed in economics and mathematics,while 50 failed in all subjects.find the number of students who failed in at least one subject
Did you try Venn diagrams?
Start filling in from the intersection of all three circles. Put 50 in that intersection, then work your way outwards from there.
Ygv h
Well, it seems like there's some serious "math-terpiece" going on here! Let's solve this puzzle.
First, let's break it down step by step:
We know that there are 300 students in total. Out of those, 50 failed in all three subjects. So, let's subtract those 50 from the total number of students:
300 - 50 = 250
Now, let's count the number of students who failed in pairs of subjects.
60 failed in economics and statistics,
64 failed in statistics and mathematics,
70 failed in economics and mathematics.
We don't want to double-count these students, so let's subtract them from the previous number:
250 - (60 + 64 + 70) = 250 - 194 = 56
Finally, we add the number of students who failed in only one subject to the result:
56 + 90 + 100 + 96 = 342
Uh-oh, it seems like we've run into a little problem here! The number of students who failed in at least one subject is larger than the total number of students in the class. We might have made a "maths-adventurous" mistake along the way!
Let's double-check our calculations and try again, shall we?
To find the number of students who failed in at least one subject, we need to add up the number of students who failed in each subject and then subtract the overlaps. Here's how we can do that step-by-step:
1. Start by adding up the number of students who failed in each subject:
- Failed in economics: 90
- Failed in statistics: 100
- Failed in mathematics: 96
2. Now, let's find the overlaps and subtract them:
- Failed in economics and statistics: 60
- Failed in statistics and mathematics: 64
- Failed in economics and mathematics: 70
To find the number of students who failed in at least one subject, we need to subtract the overlap of all three subjects:
- Failed in all three subjects: 50
3. Subtract the overlaps:
- Total number of students who failed in at least one subject = (Failed in economics) + (Failed in statistics) + (Failed in mathematics) - (Failed in economics and statistics) - (Failed in statistics and mathematics) - (Failed in economics and mathematics) + (Failed in all three subjects)
Total number of students who failed in at least one subject = (90 + 100 + 96) - (60 + 64 + 70) + 50
Simplifying the equation: Total number of students who failed in at least one subject = 286 - 194 + 50
Total number of students who failed in at least one subject = 142
So, there are 142 students who failed in at least one subject.
To find the number of students who failed in at least one subject, we need to calculate the total number of students who failed in each subject separately and also consider the overlapping failures.
First, let's calculate the number of students who failed in each subject using the information given:
- Failed in economics: 90 students
- Failed in statistics: 100 students
- Failed in mathematics: 96 students
Next, let's consider the overlapping failures:
- Failed in economics and statistics: 60 students
- Failed in statistics and mathematics: 64 students
- Failed in economics and mathematics: 70 students
Now, let's find the total number of students who failed in at least one subject. To do this, we add the number of students who failed in each subject and subtract the overlapping failures:
Total = Failed in economics + Failed in statistics + Failed in mathematics - (Failed in economics and statistics + Failed in statistics and mathematics + Failed in economics and mathematics)
Total = 90 + 100 + 96 - (60 + 64 + 70)
Total = 196
Therefore, the number of students who failed in at least one subject is 196.