Question

Everyone at your school has to take one art class, so 85 students take glass blowing, 80 students take cave painting, and 22 students take both. The wisest 95 students take photography for an easy A. How many total students are at your school?

Answer 1

To determine the total number of students at the school taking at least one art class, we use the principle of inclusion-exclusion. Considering students taking glass blowing, cave painting, both, and photography, the total comes to 238 students.

Step-by-step explanation:

To find the total number of students at the school, we need to apply the principle of inclusion-exclusion because some students are counted more than once when we simply add the numbers together. Let's define:

• A as the number of students taking glass blowing, which is 85.
• B as the number of students taking cave painting, which is 80.
• C as the number of students taking both glass blowing and cave painting, which is 22.
• D as the number of students taking the photography class, which is 95.

The total number of students taking at least one art class is given by the sum of students in each class minus the students who are counted twice because they are in both glass blowing and cave painting:

Total students = A + B - C + D

Substitute the numbers:

Total students = 85 + 80 - 22 + 95 = 238

So, there are 238 students at the school taking at least one art class.