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?

Question

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!

Answer 1

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.

Answer 2

Ohhh! Thank you!