At First, Kai Earned A Score On A Quiz. He Discovered That 5 Points Had Been Taken Off By Mistake. Kai Wrote To The Teacher, And The Teacher Removed The 5-point Deduction.Which Two Expressions Could Be Used To Find Kai's New Quiz Score? Choose BOTH
Correcting Mistakes: A Math Problem
Understanding the Problem
At first, Kai earned a score on a quiz. He discovered that 5 points had been taken off by mistake. Kai wrote to the teacher, and the teacher removed the 5-point deduction. This situation presents a common problem in mathematics where a mistake is identified and corrected. In this case, we need to find Kai's new quiz score after the correction.
Choosing the Right Expressions
To find Kai's new quiz score, we need to use expressions that represent the original score and the correction. Let's assume Kai's original score is represented by the variable x. The 5-point deduction is subtracted from the original score, resulting in a new score of x - 5. However, since the teacher removed the 5-point deduction, we need to add 5 points back to the new score.
Expression 1: Adding 5 Points to the Original Score
The first expression that could be used to find Kai's new quiz score is:
x + 5
This expression adds 5 points to the original score, effectively correcting the mistake.
Expression 2: Subtracting 5 Points from the New Score
The second expression that could be used to find Kai's new quiz score is:
(x - 5) + 5
This expression subtracts 5 points from the original score, resulting in a new score, and then adds 5 points back to correct the mistake.
Simplifying the Second Expression
We can simplify the second expression by combining the subtraction and addition operations:
x - 5 + 5 = x
This simplified expression shows that the second expression is equivalent to the original score, x.
Conclusion
In conclusion, the two expressions that could be used to find Kai's new quiz score are:
- x + 5
- (x - 5) + 5
Both expressions represent the correction of the 5-point deduction, and the second expression can be simplified to the original score, x.
Key Takeaways
- When a mistake is identified and corrected, we need to use expressions that represent the original score and the correction.
- The first expression, x + 5, adds 5 points to the original score to correct the mistake.
- The second expression, (x - 5) + 5, subtracts 5 points from the original score and then adds 5 points back to correct the mistake.
- The second expression can be simplified to the original score, x.
Real-World Applications
This problem has real-world applications in various fields, such as finance, accounting, and science. When mistakes are identified and corrected, we need to use expressions that accurately represent the correction. This problem helps to develop problem-solving skills and mathematical reasoning.
Common Mistakes to Avoid
When solving this problem, common mistakes to avoid include:
- Not identifying the mistake and correcting it.
- Using the wrong expression to find the new score.
- Not simplifying the second expression.
Tips for Solving Similar Problems
To solve similar problems, follow these tips:
- Identify the mistake and the correction.
- Use expressions that accurately represent the correction.
- Simplify the expressions to find the solution.
By following these tips and understanding the problem, you can develop problem-solving skills and mathematical reasoning to tackle similar problems.
Frequently Asked Questions (FAQs)
Q: What is the original score represented by?
A: The original score is represented by the variable x.
Q: What is the mistake that needs to be corrected?
A: The mistake is a 5-point deduction that was taken off Kai's score by mistake.
Q: How is the mistake corrected?
A: The mistake is corrected by adding 5 points back to the original score.
Q: What are the two expressions that could be used to find Kai's new quiz score?
A: The two expressions are:
- x + 5
- (x - 5) + 5
Q: Why is the second expression equivalent to the original score?
A: The second expression is equivalent to the original score because the subtraction and addition operations cancel each other out, resulting in x.
Q: What is the key takeaway from this problem?
A: The key takeaway is that when a mistake is identified and corrected, we need to use expressions that accurately represent the correction.
Q: How does this problem relate to real-world applications?
A: This problem has real-world applications in various fields, such as finance, accounting, and science, where mistakes need to be identified and corrected.
Q: What are some common mistakes to avoid when solving this problem?
A: Common mistakes to avoid include:
- Not identifying the mistake and correcting it.
- Using the wrong expression to find the new score.
- Not simplifying the second expression.
Q: What tips can be used to solve similar problems?
A: Tips for solving similar problems include:
- Identifying the mistake and the correction.
- Using expressions that accurately represent the correction.
- Simplifying the expressions to find the solution.
Q: Can you provide an example of a similar problem?
A: Here's an example:
Tom earned a score of 80 on a test. However, 10 points were deducted by mistake. Tom wrote to the teacher, and the teacher removed the 10-point deduction. What is Tom's new test score?
To solve this problem, you can use the same expressions as before:
- 80 + 10
- (80 - 10) + 10
The solution is the same as before: Tom's new test score is 90.
Q: Can you provide a visual representation of the problem?
A: Here's a visual representation of the problem:
Original Score: x Mistake: -5 Corrected Score: x + 5
This visual representation shows that the original score is represented by x, the mistake is a 5-point deduction, and the corrected score is x + 5.
Q: Can you provide a video or animation to help explain the problem?
A: Unfortunately, I'm a text-based AI and cannot provide a video or animation. However, I can provide a step-by-step explanation of the problem and its solution.
Q: Can you provide a practice problem for the reader to try?
A: Here's a practice problem:
Maria earned a score of 70 on a quiz. However, 5 points were deducted by mistake. Maria wrote to the teacher, and the teacher removed the 5-point deduction. What is Maria's new quiz score?
To solve this problem, you can use the same expressions as before:
- 70 + 5
- (70 - 5) + 5
The solution is the same as before: Maria's new quiz score is 75.