In An Examination, 75% Of The Students Passed. The Number Of Students Who Passed Was 240. How Many Students Failed?A. 70 B. 75 C. 80 D. 90

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In this article, we will delve into a mathematical problem that involves percentages and proportions. The problem states that 75% of the students passed an examination, and the number of students who passed was 240. We are required to find the number of students who failed.

The Given Information

  • 75% of the students passed the examination.
  • The number of students who passed was 240.

The Unknown Quantity

  • The number of students who failed the examination.

Step 1: Understanding the Percentage

To begin solving this problem, we need to understand the concept of percentages. A percentage represents a value as a fraction of 100. In this case, 75% means that 75 out of every 100 students passed the examination.

Step 2: Setting Up the Equation

Let's assume that the total number of students is represented by the variable 'x'. Since 75% of the students passed, we can set up the following equation:

75% of x = 240

To convert the percentage to a decimal, we divide by 100:

0.75x = 240

Step 3: Solving for x

Now, we need to solve for 'x' by dividing both sides of the equation by 0.75:

x = 240 / 0.75 x = 320

So, the total number of students is 320.

Step 4: Finding the Number of Students Who Failed

Since 75% of the students passed, the number of students who failed is the remaining 25%. We can find this by subtracting the number of students who passed from the total number of students:

Number of students who failed = Total number of students - Number of students who passed = 320 - 240 = 80

Therefore, the number of students who failed is 80.

Conclusion

In this article, we analyzed a mathematical problem that involved percentages and proportions. By setting up an equation and solving for the unknown quantity, we were able to find the number of students who failed the examination. The correct answer is 80.

Key Takeaways

  • Understanding percentages and proportions is crucial in solving mathematical problems.
  • Setting up equations and solving for unknown quantities is an essential skill in mathematics.
  • By breaking down complex problems into smaller, manageable parts, we can arrive at the correct solution.

Frequently Asked Questions

  • What is the meaning of 75% in the context of the problem?
    • 75% represents the proportion of students who passed the examination.
  • How do we convert a percentage to a decimal?
    • We divide the percentage by 100 to convert it to a decimal.
  • What is the total number of students in the examination?
    • The total number of students is 320.

References

In the previous article, we analyzed a mathematical problem that involved percentages and proportions. We set up an equation and solved for the unknown quantity to find the number of students who failed the examination. In this article, we will provide a comprehensive guide to frequently asked questions related to the problem.

Q&A: Understanding the Problem

Q: What is the meaning of 75% in the context of the problem?

A: 75% represents the proportion of students who passed the examination.

Q: How do we convert a percentage to a decimal?

A: We divide the percentage by 100 to convert it to a decimal.

Q: What is the total number of students in the examination?

A: The total number of students is 320.

Q: How do we set up an equation to solve for the unknown quantity?

A: We use the following equation:

75% of x = 240

To convert the percentage to a decimal, we divide by 100:

0.75x = 240

Q: How do we solve for x?

A: We divide both sides of the equation by 0.75:

x = 240 / 0.75 x = 320

Q: What is the number of students who failed the examination?

A: The number of students who failed is the remaining 25%. We can find this by subtracting the number of students who passed from the total number of students:

Number of students who failed = Total number of students - Number of students who passed = 320 - 240 = 80

Q&A: Solving the Problem

Q: What is the first step in solving the problem?

A: The first step is to understand the concept of percentages and proportions.

Q: How do we set up the equation?

A: We use the following equation:

75% of x = 240

Q: What is the next step after setting up the equation?

A: We convert the percentage to a decimal by dividing by 100:

0.75x = 240

Q: How do we solve for x?

A: We divide both sides of the equation by 0.75:

x = 240 / 0.75 x = 320

Q: What is the final step in solving the problem?

A: We find the number of students who failed by subtracting the number of students who passed from the total number of students:

Number of students who failed = Total number of students - Number of students who passed = 320 - 240 = 80

Q&A: Tips and Tricks

Q: What is the most important thing to remember when solving the problem?

A: The most important thing to remember is to understand the concept of percentages and proportions.

Q: How do we avoid making mistakes when solving the problem?

A: We can avoid making mistakes by double-checking our calculations and using a calculator to verify our answers.

Q: What is the best way to approach the problem?

A: The best way to approach the problem is to break it down into smaller, manageable parts and to use a step-by-step approach.

Conclusion

In this article, we provided a comprehensive guide to frequently asked questions related to the problem. We covered topics such as understanding the problem, setting up the equation, solving for x, and finding the number of students who failed. We also provided tips and tricks for avoiding mistakes and approaching the problem. By following these guidelines, you can confidently solve the problem and arrive at the correct solution.

Key Takeaways

  • Understanding percentages and proportions is crucial in solving mathematical problems.
  • Setting up equations and solving for unknown quantities is an essential skill in mathematics.
  • By breaking down complex problems into smaller, manageable parts, we can arrive at the correct solution.

References