Solving the Student Exam Problem: A Comprehensive Guide
Often, we encounter problems related to the number of students passing or failing an exam, and the task is to determine the total number of students who took the exam. In this article, we will solve the problem where 72 students passed, and 392 students failed. We'll explore the different methods and calculations to find the total number of students who took the exam.
Method 1: Using Algebraic Equations
Let the total number of students be represented by ( x ).
According to the problem, 72 students passed the exam which means the number of students who failed is ( x - 72 ).
Since 392 students failed, we can express the number of students who failed as ( 0.28x 392 ).
To find ( x ), we rearrange the equation:
( x frac{392}{0.28} )
Calculating the value of ( x ) gives:
( x 1400 )
Hence, the total number of students is 1400.
Method 2: Using Percentage with Given Values
Another approach is to use the percentage method:
Given that 72 students passed the exam, and 392 students failed, we can calculate the percentage of the total students who failed.
( text{Percentage of failed students} frac{392}{x} times 100 )
We know that 72 students passed, and the remaining 28% of the students failed. So:
( 72 392 x )
( 464 72 0.28x )
( 0.28x 392 )
( x frac{392}{0.28} 1400 )
The total number of students is 1400.
Additional Method: Using Direct Proportion
Another method involves using direct proportion:
We know that 72 students passed, and 72 392 464 students in total. If 28% of the total students failed, we can use the equation:
( frac{392}{x} frac{28}{100} )
( x frac{392 times 100}{28} )
( x 1400 )
Hence, the total number of students is 1400.
Conclusion
From the various methods explored above, we can conclude that the total number of students who took the exam is 1400. Each approach validates the same result, providing a comprehensive solution to the problem of determining the total number of students based on pass and fail counts.
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