How Many Students Passed the Exam: A Comprehensive Guide
Introduction
In educational settings, it is common to encounter situations where the percentage of students who pass and fail an exam is provided, and one needs to determine the actual number of students who passed or failed. This guide aims to explain the process of calculating the number of passed students using different approaches, including fractions, percentages, and algebraic methods. Let's dive into the details.Percentage Calculation Method
First, let's consider the scenario where in class 93 of students pass and 72 students fail. We aim to find out how many students passed the exam using percentages. Here's how you can solve it:Problem Statement
In a class, 93 of students passed and 72 students failed. How many students passed the exam?Solution
First, let's calculate the percentage of students who failed:Percentage of Failed Students (frac{72}{180} times 100)
Since 180 is the sum of students who passed and failed:
Percentage of Failed Students (frac{72}{180} times 100 40%)
Therefore, 60% of the class passed the exam:
Number of Students Passed (frac{60}{100} times 93 55.8 approx 56) students
So, 56 students passed the exam.
Fraction and Percentage Method
Another approach uses fractions and percentages. Here is an example where there are 20 students, 14 passed and 6 failed. This method involves working with fractions to determine the number of students who passed or failed.Problem Statement
In a class, 20 students took an exam. If 14 students passed and 6 students failed, calculate the total number of students in the class and the percentage of students who passed and failed.Solution
Total number of students 20 Percentage of Students Who Passed (frac{14}{20} times 100 70%) Percentage of Students Who Failed (frac{6}{20} times 100 30%)Algebraic Method
The algebraic method provides a step-by-step approach to solving the problem. Here, we use simple algebra to solve for the total number of students and the number of students who passed.Problem Statement
Seventy percent of the class passed the exam. Therefore, thirty percent of the class failed the test. Thirty percent is ( frac{3}{10} ).Solution
Let the total number of students be ( x ).Number of Students Passed ( x times frac{70}{100} frac{7x}{10} )
Using the given information, we set up the equation:
(frac{7x}{10} - x -18 )
Solving the equation:
( frac{-3x}{10} -18 )
( x 60 )
So, the total number of students in the class is 60.
Number of Students Passed (70% times 60 42)
Number of Students Failed (60 - 42 18)
Multiple Approaches
Let's consider another scenario where in a class, 93 students passed and 72 students failed. We aim to find out the total number of students in the class using multiple approaches.Problem Statement
In a class, 93 students passed and 72 students failed. Calculate the total number of students in the class and the number of students who passed and failed.Solutions
1. **Percentage Method**Total Number of Students (frac{18}{30} times 100 60)
Number of Students Passed 70% of 60 42
Number of Students Failed 60 - 42 18
2. **Algebraic Method**Let the total number of students be ( x ).
Using the given information:
( frac{7x}{10} - x -18 )
Solving the equation:
( frac{-3x}{10} -18 )
( x 60 )
So, the total number of students in the class is 60.
Number of Students Passed (70% times 60 42)
Number of Students Failed (60 - 42 18)