Solving Word Problems: How to Determine the Total Number of Questions on an Exam

Word problems are an integral part of math education, helping students develop critical thinking and problem-solving skills. This article explores a specific type of word problem, focusing on how to determine the total number of questions on an exam based on the information provided. We'll break down the problem step by step, providing a clear, practical example that can be easily understood and applied.

Understanding the Problem

The problem at hand is as follows: a student answered 12 questions correctly, which represents 80% of the total number of questions on the test. The task is to determine the total number of questions on the exam. Let's walk through the steps to solve this problem.

Setting Up the Equation

To solve this problem, we need to set up an equation based on the information given. Let's denote the total number of questions on the test by x. According to the problem statement, 80% of x equals 12 questions. We can express this as:

0.8x 12

Solving the Equation

Now, we need to solve for x. To do this, we'll isolate x by dividing both sides of the equation by 0.8:

[x frac{12}{0.8}]

Calculating the right-hand side will give us the total number of questions:

[x 15]

Conclusion

Therefore, the total number of questions on the exam is 15. This example not only provides a straightforward solution but also demonstrates the step-by-step process of solving a word problem involving percentages. By understanding and applying this method, students can tackle similar problems with confidence.

Remember, the key to solving word problems is to carefully read the problem, identify the given information, and set up the appropriate equations. Practice is essential to improving your problem-solving skills. Whether you're a student or a teacher, engaging with such exercises can significantly enhance your mathematical abilities.

Additional Practice

For further practice, consider the following similar problems to reinforce your understanding:

15 questions were on the exam. If a student answered 8 questions correctly, what percentage does this represent? A teacher gave a test with 20 questions. If a student answered 16 questions correctly, what is the student's percentage score? In a math test, a student answered 24 questions out of 30. What is the student's score as a percentage?

By working through these additional problems, you can solidify your understanding of how to apply the same principles to different scenarios. Happy solving!