Answer:
To determine whether Levi's reasoning is correct, we need to analyze the ratio of correct answers to total questions before and after he answered the additional three questions correctly.
Before answering the additional three questions, Levi had answered 8 out of 10 questions correctly. This means his ratio of correct answers to total questions was 8/10 or 0.8.
Now, let's consider what happens when Levi answers the next three questions correctly. He adds these three correct answers to both the total number of questions and his correct responses. Therefore, his new totals become 11 questions in total and 11 correct answers.
To check if the ratio remains the same, we divide the number of correct answers by the total number of questions: 11/11 = 1.
Comparing the two ratios, we can see that before answering the additional three questions, Levi had a ratio of 0.8, while after answering them correctly, his ratio became 1. These ratios are not equal, indicating that Levi's reasoning is incorrect.
Levi's assumption that adding three to both the total number of questions and his correct responses would maintain the same ratio is flawed. The reason for this is that when adding an equal number to both the numerator and denominator of a fraction, it does not guarantee that the ratio will remain unchanged.
In this case, adding three to both the numerator and denominator resulted in a different ratio because the increase in both values was not proportional. The numerator increased by three units, while the denominator increased by one unit. This imbalance caused a change in the overall ratio.
Therefore, Levi's reasoning is incorrect as adding three to both the total questions and correct responses does not maintain the same ratio of correct answers to total questions.
In conclusion, Levi's assumption about maintaining the same ratio is incorrect because adding an equal number to both the numerator and denominator does not guarantee that the ratio will remain unchanged.
Explanation: