The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 32 said they had taken physics, 51 said they had taken chemistry and 15 said they had taken both. Ten said they had taken neither. How many recent high school grads were surveyed?

Can you explain why 6 different math posts, each with a different name, came from the same computer in the last 10 minutes?

I'm totally lost and I didn't want to continue posting under my name tootie. Thinking that I wouldn't get the help since I had too many posts

Not at all. What you're doing will lose continuity. Tutors have to explain things over on the same subject for a different person, or keep referring to a previous post. It is much more efficient for you and for tutors to refer to the same screen name.

State as followings:

P(P) = #students take physics = 32
P(C) = #students take chemistry = 51
P(P and C) = 15
P(neither) = 10
Total students = P(P) + P(C) - P(P and C) + P(neither) = 78

To find the total number of recent high school grads surveyed, we need to add up the number of students who took physics, the number who took chemistry, the number who took both, and the number who took neither.

Let's start by finding the number of students who took either physics or chemistry. We can do this by adding the number of students who took physics (32) and the number who took chemistry (51):

32 + 51 = 83

However, this includes the students who took both physics and chemistry. To get the number of students who took either physics or chemistry, we need to subtract the number who took both (15):

83 - 15 = 68

Now, we need to add the number of students who took neither physics nor chemistry, which is given as 10:

68 + 10 = 78

Therefore, 78 recent high school grads were surveyed.