at the state spelling bee, there were 120 students. one-fourth of the students were eliminated during the first round. one-third of the remaining students were eliminated during the second round. two-thirds of the remaining students were eliminated during the third round. how many students were left after the third round?
3/4 * 120 = 90 after first round
2/3 * 90 = 60 after second round
1/3 * 60 = ____ after third round
answer is 20
Poop ×pee
I'm not understanding
To find out how many students were left after the third round, we need to follow these steps:
Step 1: Find out how many students were eliminated in each round.
- In the first round, one-fourth of the total students were eliminated. To find this, we need to calculate 1/4 of 120 students.
1/4 * 120 = 30 students
- In the second round, one-third of the remaining students were eliminated. So, if 30 students were eliminated in the first round, we need to calculate 1/3 of the remaining students.
Remaining students = Total students - Eliminated students from the first round = 120 - 30 = 90 students
1/3 * 90 = 30 students
Therefore, 30 students were eliminated in the second round.
- In the third round, two-thirds of the remaining students were eliminated. So, we need to calculate 2/3 of the students who were left after the second round.
Remaining students after the second round = Total students - Eliminated students from the first round - Eliminated students from the second round
Remaining students = 120 - 30 - 30 = 60 students
2/3 * 60 = 40 students
Therefore, 40 students were eliminated in the third round.
Step 2: Calculate the number of students left after the third round.
To calculate the number of students left, subtract the eliminated students from the total number of students.
Remaining students after the third round = Total students - Eliminated in the third round
Remaining students = 120 - 40 = 80 students
Therefore, after the third round, there are 80 students left.