Aclass has 30 students,17 have taken science,19 have taken arts and two students have enrolled in any course. how many students enrolled in both science and arts ?

Let x = number of students enrolled in both Science and Arts.

Then the number of students taking Science only is 17 – x and,
the number of students taking Arts only is 19 – x.

We know that
Total # of students in class = # Science only + # Arts only + Both Arts & Sciences + # Any
= (17 – x) + (19 – x) + x + 2
= 38 + x

This should be equal to 30 as given. So,
38 – x = 30

Subtract 38 from both sides:
–x = –8

So x = 8.

8