To compare the scores of Austin and Liz, let's first determine how many questions Austin answered correctly based on his percentage and how many Liz answered.
-
Austin's Score:
- Austin answered 92% of the questions correctly. However, we need to know the total number of questions he attempted. Assume the total questions on the quiz are \(x\).
- Therefore, the number of questions he answered correctly would be \(0.92x\).
-
Liz's Score:
- Liz answered 47 out of 50 questions correctly, which is straightforward:
- Her percentage score is \(\frac{47}{50} \times 100 = 94%\).
Next, we need to compare Austin's correct answers \(0.92x\) with Liz's score.
Since Liz scored 94%, we'll set up the comparison by analyzing Austin's correct answers in relation to the total number of questions. We need to see if there is a reasonable value for \(x\) where Austin's correct answers can be below or above Liz's 47 correct answers.
-
If \(x = 50\) (the same as Liz):
- Austin's correct answers = \(0.92 \times 50 = 46\).
- In this case, Liz (47) scored higher than Austin (46).
-
If \(x > 50\):
- For example, if \(x = 60\), then:
- Austin's correct answers = \(0.92 \times 60 = 55.2\), which means he answered approximately 55 questions correctly.
- Here, Austin (55) would have a higher score than Liz (47).
From this, we can conclude:
- If the total number of questions for Austin is fewer than 50, he would score fewer correct answers than Liz.
- If the total number of questions for Austin is 50, he would have answered fewer correctly (46), thus Liz scored higher.
- If the total is more than 50, Austin might score higher.
However, generally speaking, we have established that Liz answered a greater number of questions correctly than Austin if both are compared with the same total questions (assuming \(x = 50\)).
Thus, the best fit answer would be:
B. Austin answered 47 of the questions correctly, which is less than 92%, so Liz earned the higher score.
(Note: B's wording says Austin answered 47 questions, which is incorrect; he answered 46 when calculated for 50 total questions. The closest comparable option is taken considering the context).
1 answer