Question

Translate to an equation and solve. Willis scored \(85 \%\) on a test with 40 questions. a. How many questions did he answer correctly? b. What percent did he answer incorrectly? c. How many questions did he answer incorrectly?

Short answer

Answer: Willis answered 34 questions correctly, 6 questions incorrectly, and the percentage of incorrect answers is 15%.

Step-by-step solution

Find the number of correct answers

To find the number of correct answers, multiply the total number of questions (40) by the percentage of correct answers (85%). Write it as an equation: Correct answers = Total questions * Correct answers percentage

Calculate the number of correct answers

Substitute the given values into the equation: Correct answers = 40 * 0.85 = 34 So, Willis answered 34 questions correctly. a. Willis answered 34 questions correctly.

Calculate the percentage of incorrect answers

Now, we need to find the percentage of incorrect answers. Since he answered 85% of the questions correctly, the remaining percentage of questions he answered incorrectly is: Incorrect answers percentage = 100% - Correct answers percentage

Solve for the percentage of incorrect answers

Substitute the given value: Incorrect answers percentage = 100% - 85% = 15% b. Willis answered 15% of the questions incorrectly.

Find the number of incorrect answers

To find the number of incorrect answers, multiply the total number of questions (40) by the percentage of incorrect answers (15%). Write it as an equation: Incorrect answers = Total questions * Incorrect answers percentage

Calculate the number of incorrect answers

Substitute the given values into the equation: Incorrect answers = 40 * 0.15 = 6 c. Willis answered 6 questions incorrectly.

Key concepts

Percentage Calculation

Understanding how to calculate percentages is essential for interpreting scores, financial data, and other measurements in everyday life. When solving percentage problems, like determining how many questions Willis answered correctly on a test, the key is to convert the percentage into a decimal and then apply multiplication. For example, Willis scored 85%, which you can write as 0.85 in decimal form.

To find out the number of correct answers, you multiply the total number of questions (40 in this case) by 0.85. This equation translates percentage knowledge into a tangible number of correct answers, which is critical for test scoring. It's important to recognize that multiplying by 0.85 is the same as finding 85% of 40, the core concept in percentage calculations.

Equation Translation

Equation translation is a process of converting a real-world situation into a mathematical expression. For example, 'Willis scored 85% on a test with 40 questions' translates to the equation 'Correct answers = 40 * 0.85.' This translation helps us quantify the problem for easier mathematical manipulation and problem-solving, allowing us to reach the result more systematically.

Learning to create and interpret these equations is crucial for students to apply mathematical concepts in practical scenarios such as test scoring. The equation serves as a blueprint for the calculation needed to find the result, effectively bridging the gap between the conceptual understanding of percentages and their practical application.

Test Scoring

Test scoring often involves percentages, as seen with Willis’ exam results. To navigate this, one must understand not only how to calculate percentages but also how to interpret them in the context of test results. After calculating the number of correct and incorrect answers, you can determine the test score.

If Willis answered 34 questions correctly out of 40, we express this as the percentage he got right (which is given as 85%). But to figure out what percentage he got wrong, we subtract the percentage correct from 100%, getting 15%. Hence, test scoring involves both calculation and interpretation of percentages to yield a comprehensive understanding of performance.

Mathematical Problem-Solving

Mathematical problem-solving encompasses identifying the problem, translating it into a mathematical equation, and then solving that equation. The scenario of Willis’ test performance illustrates this concept. Once we have translated the real-world details into the language of mathematics, as shown in the 'equation translation' concept, we can solve for the unknown quantities.

In Willis’ case, we are firstly solving for the number of correct and incorrect answers and then for the percentages related to each. This demonstrates that mathematical problem-solving not just involves numerical calculations but also a logical approach to dissecting the problem into solvable steps – a strategy applicable to an array of mathematical challenges faced by students.