Hello! I have a quiz coming up and have been struggling with a certain type of problem on all of my quick checks. I've read through all of the lessons, and still can't figure out how to do the problem! Can someone explain how to solve the problem for me?
In a school of 464 students, 89 students are in the band, 215 students are on sports teams, and 31 students participate in both activities.
How many students are involved in neither band nor sports?
A. 160 students
B. 191 students
C. 249 students
D. 433 students
(I answered "A" on my quick check, but the correct answer was "B")
Thank you!
you did 464 - 89 - 215 = 160
but the 31 are included in the 89, as well as the 215,
so you subtracted the 31 twice
just add it back on once
464 - 89 - 215 + 31 = 191
You could do this also with a Venn diagram to see the answer.
Ohhh! Thank you!
Sure! I can help you with that problem. To find the number of students involved in neither band nor sports, we need to subtract the number of students in the band, the number of students on sports teams, and the number of students who participate in both activities from the total number of students.
First, let's find the number of students involved in either band or sports:
Total number of students in the band = 89
Total number of students on sports teams = 215
To find the number of students involved in either band or sports, we add these two numbers together:
89 + 215 = 304
Now, let's subtract the number of students who participate in both activities. We already know that 31 students participate in both band and sports, so we subtract this number from the total:
304 - 31 = 273
Now, to find the number of students involved in neither band nor sports, we subtract this number from the total number of students in the school:
464 - 273 = 191
Therefore, the correct answer is B. 191 students are involved in neither band nor sports.
I hope this explanation helps you understand how to solve the problem. Good luck on your quiz!