Of the 196 students in the entering class at Lakeside Community College, 100 of them plan to participate in sports, 85 in student government, and 55 in the theater arts. 27 indicated they would participate in sports and student government, 24 in sports and theater arts, 14 in student government and theater arts, and 10 said they will take part in all three of the extracurricular activities. How many will not participate in any of the three extracurricular activities?

The answer is 41

Step-by-step explanation:

Let's write some variables:

x: students who only participate in sports.

y: students who only participate in government.

z: students who only participate in theater.

Then:

1) we have 27 students participate in sports and government.

2) we have 24 students participate in sports and theater.

3) we have 14 students participate in government and theater.

4) we have 10 students participate in sports, government and theater.

Also, We have that 100 students participate in sports so ...

100 = x + 27 + 24 + 10

x = 39

Also, We have that 85 students participate in government so ...

85 = y + 27 + 14 + 10

x = 34

Also, We have that 55 students participate in theater so ...

55 = y + 24 + 14 + 10

x = 7

At the end the total of students who are participating in sports, government or theater are:

39 + 34 + 7 + 27 + 24 + 14 + 10 = 155

But there are 196 students in the class so the rest of students who are not participating are:

196 - 155 = 41