A class of 30 students took two quizzes. Sixteen passed the first quiz and 20 passed the second quiz. If four students failed both quizzes, how many pass both?
make a Venn diagram
let the number who passed both tests be x
fill in the values given,
then
(16-x) + x + (20-x) + 4 = 30
-x = -6
x = 6
uhmm.. I think the answer is 10.
To find out how many students passed both quizzes, we need to subtract the number of students who failed both quizzes from the total number of students who passed at least one quiz.
Let's break it down step by step:
Step 1: Find the total number of students who passed at least one quiz
We know that 16 students passed the first quiz and 20 students passed the second quiz. To find the total number of students who passed at least one quiz, we add these two numbers:
16 + 20 = 36
Step 2: Subtract the number of students who failed both quizzes
We were given that 4 students failed both quizzes. To find the total number of students who passed both quizzes, we subtract this number from the total number of students who passed at least one quiz:
36 - 4 = 32
Therefore, 32 students passed both quizzes.
To find out how many students passed both quizzes, we can use the principle of inclusion-exclusion.
First, we know that 16 students passed the first quiz and 20 students passed the second quiz. However, we also know that 4 students failed both quizzes, so we need to subtract these 4 students from the total count.
If we add the number of students who passed the first quiz (16) and the number of students who passed the second quiz (20), we get 36. However, this count includes the students who passed both quizzes twice. So, we need to subtract the number of students who passed both quizzes twice to get the correct count.
Since we know that 4 students failed both quizzes, we can subtract this count from the total count of passing students from both quizzes. Therefore, the number of students who passed both quizzes is 36 - 4 = 32.
Hence, 32 students passed both quizzes.