SOLUTION: The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 75 said they had taken physics, 121 said

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Question 307189: The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 75 said they had taken physics, 121 said they had taken chemistry and 11 said they had taken both. Fifteen said they had taken neither. How many recent high school grads were surveyed?
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The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 75 said they had taken physics, 121 said they had taken chemistry and 11 said they had taken both. Fifteen said they had taken neither. How many recent high school grads were surveyed?
Thank you

Let P be the number of those who took physics
Let C be the number of those who took chemistry
P = 75
C = 121
Since the number of students who took both courses is 11, the number who took physics only is 75 - 11 - 64 and C only is 121 - 11 = 110.
Since 15 took neither we have for the total number of students:
Physics only + Chemistry only + both + neither =
64 + 110 + 11 + 15 = 200.