On a 10-question online quiz, you correctly answer four 1-point questions and five 2-point questions. You earn 87.5% of the possible points on the quiz.
a. How many possible points is the quiz worth?
a
b. How many questions did you miss?
a
How many points was each missed question worth?
p = points
a.
4 ∙ 1 + 5 ∙ 2 = 14
14 = 87.5% = 0.875 p
p = 14 / 0.875 = 15
b.
10-question
Correctly answers = 4 ( 1-point questions ) + 5 ( 2-point questions ) =
4 + 5 = 9 Correctly answers
10 - 9 = 1
c.
100% - 87.5% = 12.5% = 12.5 / 100 = 0.125
0.125 ∙ 16 = 2
My typo.
p = 14 / 0.875 is not 15
p = 14 / 0.875 = 16
a. To find out how many possible points the quiz is worth, we can use the percentage of points earned. Since you earned 87.5% of the possible points on the quiz, this means you earned 87.5 points out of a total possible points.
Let's assume the total possible points on the quiz is "x."
Therefore, we can set up the following equation:
87.5% of x = 87.5
To solve for x, we can divide both sides of the equation by 87.5% (or 0.875):
x = 87.5 / 0.875
x = 100
Therefore, the quiz is worth a total of 100 points.
b. To find out how many questions you missed, we need to subtract the number of questions you answered correctly from the total number of questions on the quiz.
Let's assume the total number of questions on the quiz is "y."
Therefore, we can set up the following equation:
4 correct 1-point questions + 5 correct 2-point questions + Number of missed questions = Total number of questions
4 + 5 + Number of missed questions = y
Since we know that there are 10 questions in total on the quiz, we can substitute y with 10:
4 + 5 + Number of missed questions = 10
Simplifying the equation:
9 + Number of missed questions = 10
Subtracting 9 from both sides of the equation:
Number of missed questions = 10 - 9
Number of missed questions = 1
Therefore, you missed 1 question on the quiz.
c. Since you missed 1 question, we can determine the points each missed question was worth by subtracting the points earned from the maximum points possible.
Maximum points possible = Total questions * Maximum points per question
Maximum points possible = 10 * 2 (assuming each question is worth 2 points)
Maximum points possible = 20
Points for missed questions = Maximum points possible - Points earned
Points for missed questions = 20 - 87.5
Points for missed questions = 32.5
Therefore, each missed question was worth 32.5 points.
To find the answers to these questions, we can use a system of equations.
Let x represent the number of 1-point questions and y represent the number of 2-point questions on the quiz.
a. The total possible points on the quiz can be calculated by multiplying the number of 1-point questions by 1 and the number of 2-point questions by 2:
Total possible points = (x * 1) + (y * 2)
b. The number of questions missed can be calculated by subtracting the number of correct answers from the total number of questions:
Number of questions missed = 10 - (number of correct 1-point questions + number of correct 2-point questions)
We can use these equations to solve for x and y.
Given that you correctly answered four 1-point questions and five 2-point questions, we substitute these values into the equations.
a. The total possible points can be calculated as:
Total possible points = (4 * 1) + (5 * 2) = 4 + 10 = 14
b. The number of questions missed can be calculated as:
Number of questions missed = 10 - (4 + 5) = 10 - 9 = 1
To find the points for each missed question, we can divide the total possible points by the number of questions:
Points for each missed question = Total possible points / Number of questions missed = 14 / 1 = 14
Therefore, the quiz is worth 14 possible points, you missed 1 question, and each missed question is worth 14 points.