In a test for every 6 answers carlene got correct, she got 2 wrong. She got 54 correct answers.
1 how many questions did the test have?
2 express the number of questions she answered correct as a percentage.
ratio of correct to wrong = 6 : 2 = 3 : 1
= 3x : x
total questions = 4x
given: 3x = 54
x = 18
so there were 4(18) or 72 questions
percentage correct = 54/72
= .75 or 75%
we could have seen that from the top
correct = 3x, total = 4x
percentage correct = 3x/4x = 3/4 = .75
To find the number of questions in the test, we need to first determine the ratio of correct answers to wrong answers. We are given that for every 6 correct answers, Carlene got 2 wrong. This means the ratio of correct answers to wrong answers is 6:2, which simplifies to 3:1.
1. To find the total number of questions, we need to consider that the ratio 3:1 represents the entire set of questions. So, for every 3 parts (representing correct answers), there is 1 part (representing wrong answers). Since we know Carlene got 54 correct answers, we can set up a proportion:
3 parts (correct answers) / 1 part (wrong answers) = 54 correct answers / x total questions
Cross multiplying gives us:
3 * x = 1 * 54
3x = 54
x = 54 / 3
x = 18
Therefore, the test had a total of 18 + 6 = 24 questions.
2. To express the number of questions Carlene answered correctly as a percentage, we divide the number of correct answers by the total number of questions and multiply by 100.
Percentage = (Number of correct answers / Total number of questions) * 100
Percentage = (54 / 24) * 100
Percentage = 225%
Therefore, Carlene answered 225% of the questions correctly.