How to Solve a Science Quiz Scoring Puzzle: A Step-by-Step Guide

Mathematics often intersects with real-life scenarios in unexpected ways. One such example is a common quiz with a specific scoring system. This article is designed to help you understand and solve the puzzle of Samuel's quiz score using a step-by-step approach. Whether you're a student preparing for a quiz or a professional brushing up on your problem-solving skills, this guide will walk you through the solution.

The Quiz Scoring System

In a science quiz, 2 marks are awarded for every correct answer, and 1 mark is deducted for every wrong answer. Samuel, a participant in the quiz, found out that he got ( frac{1}{6} ) of the quiz wrong. This means that for every 6 questions, 1 was incorrect and the remaining 5 were correct.

Understanding the Variables

To start solving the problem, let ( x ) represent the total number of questions on the quiz.

Number of Wrong Answers

Given that Samuel got ( frac{1}{6} ) of the quiz wrong:

Wrong answers ( frac{1}{6}x )

Number of Correct Answers

Since the rest of the questions were answered correctly:

Correct answers ( x - frac{1}{6}x frac{5}{6}x )

Setting Up the Equation

The scoring system combines the marks awarded for correct answers and those deducted for wrong answers. We can represent this mathematically as follows:

Score 2 times; Correct answers - 1 times; Wrong answers

Substituting the expressions we found:

Score 2 times; ( frac{5}{6}x ) - 1 times; ( frac{1}{6}x )
( frac{10}{6}x - frac{1}{6}x )

Simplifying the equation:

Score ( frac{1 - x}{6} frac{9x}{6} frac{3}{2}x )

We know from the problem statement that Samuel scored 90 marks. Therefore, we set up the equation:

( frac{3}{2}x 90 )

To solve for ( x ), multiply both sides by ( frac{2}{3} ):

( x 90 times frac{2}{3} 60 )

Hence, the total number of questions in the quiz is 60.

Verifying the Solution

Let's verify the solution using a practical approach. We can create a worksheet with the following columns:

Questions Correct Wrong Score

Starting with the following initial values:

20 questions, which means Samuel got ( frac{5}{6} times 20 16.67 ) correct and ( frac{1}{6} times 20 3.33 ) wrong, resulting in a score of 2 times; 16.67 - 1 times; 3.33 30.

By increasing the number of questions to 60, we can systematically solve the problem:

With 60 questions, Samuel got ( frac{5}{6} times 60 50 ) correct and ( frac{1}{6} times 60 10 ) wrong. Substituting these values into the score formula:

Score 2 times; 50 - 1 times; 10 100 - 10 90

This confirms our solution, highlighting that Samuel indeed scored 90 marks on the quiz with 60 questions.

Conclusion

This problem not only demonstrates the application of algebraic equations but also emphasizes the importance of logical reasoning and step-by-step problem-solving skills. Whether you're tackling math problems or real-world challenges, understanding the underlying concepts and breaking down the problem into manageable steps is key.

Remember, the journey to finding the solution is as valuable as the solution itself. Practice and patience are your best tools in mastering such problems. If you found this article helpful, consider sharing it with friends or classmates who may need similar guidance. Happy solving!