A quiz has 20 questions with 5 points awarded for each correct answer and one point deducted for each incorrect answer, with 0 for each question omitted, Larry scored 72 points. How many questions did he omit?
number correct --- x , 0 ≤ x ≤ 20
number wrong ---- y
number skipped ---- 20-x-y
5x - y + 0 = 72
y = 5x - 72
y ≥ 0
if x = 14, y = -2 , not possible
if x = 15 , y = 3 , skipped = 2
if x = 16, y = 8 , not possible , x+y>20
so he got 16 right, 8 wrong, and skipped 2
check:
5(16) - 1(8) + 0 = 72
To find out how many questions Larry omitted, we need to first calculate the maximum possible score he could have achieved by answering all the questions correctly.
Since there are 20 questions, and each question is worth 5 points, the maximum possible score is 20 * 5 = 100 points.
However, Larry's score is 72 points, which means he must have had some incorrect answers or omitted questions.
Next, we need to determine the number of incorrect answers Larry had. Each incorrect answer results in a deduction of 1 point.
Let's assume Larry had x incorrect answers. In that case, his score would be reduced by x points.
So, his adjusted score would be 100 - x.
Given that his actual score is 72, we can set up the equation 100 - x = 72.
Rearranging this equation, we have x = 100 - 72 = 28.
Hence, Larry must have had 28 incorrect answers.
Now, to calculate the number of questions Larry omitted, we know that each omitted question is scored as 0 points.
So, if Larry omitted y questions, his score would be reduced by y points.
Based on the given information, his score of 72 is already adjusted for incorrect answers, so y = 72.
Therefore, Larry omitted 72 questions.