Question

1. in a trivia game, levi answered 8 questions correctly out of 10 turns in the game. he then answered the next three questions correctly. he reasoned that because he added 3 to both the total questions and his correct responses, that the ratio of correct answers to total questions remained the same. is he correct? justify your response.

Explanation:

Step1: Calculate initial ratio

Initial correct answers = 8, initial total turns = 10. Initial ratio = $\frac{8}{10} = \frac{4}{5} = 0.8$.

Step2: Calculate new ratio

New correct answers = 8 + 3 = 11, new total turns = 10 + 3 = 13. New ratio = $\frac{11}{13} \approx 0.846$.

Step3: Compare ratios

Since $0.8
eq 0.846$, the ratios are different.

Answer:

Levi is not correct. The initial ratio of correct answers to total questions is $\frac{8}{10} = 0.8$, and the new ratio after answering 3 more questions correctly is $\frac{11}{13} \approx 0.846$. These two ratios are not equal, so the ratio does not remain the same.