The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 90 said they had taken physics, 138 said they had taken chemistry and 45 said they had taken both. Thirty-two said they had taken neither. How many recent high school grads were surveyed?

Question

305??

Answer 1

By the inclusion-exclusion principle, the number of grads who have taken at least one of Chemistry or Physics is:
n(P)+n(C)-n(P∩C)
Add this to those who have taken neither is the total number of grads.

Answer 2

(90) + (138) - (48) = 180 + 32 = 212 ??

Answer 3

Correct.
Try to see why it works with the help with the help of a Venn diagram.

Answer 4

thanks a million!

Answer 5

Keep up the good work!