The National Association for Women in Science asked recent high school grads if they had taken certain science classes. Of those surveyed, 23 said they had taken physics, 47 said they had taken chemistry and 5 said they had taken both. Seven said they had taken neither. How many recent high school grads were surveyed?
use Venn diagrams.
draw two intersecting circles, label one P , the other C
place 5 in the intersection of the two circles
place 18 in the P circle outside the intersection, (notice you have a total of 23 in P)
place 42 in the C circle outside the intersection,
(notice you have a total of 47 in C)
add them up: 18+5+42 = 65
or
N(P OR C) = N(P) + N(C) - N(P AND C)
= 23+47-5
= 65
hmmmmmm im kind of getting it.....but for some reason when i did it my answer was 72....geometry is not my best subject haha
72 is right. Reiny forgot to add 7 who said they had taken neither.
65 + 7 = 72
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 of students who took chemistry, the number of students who took both, and the number of students who took neither, and do some calculations.
Let's break down the given information:
- Number of students who took physics = 23
- Number of students who took chemistry = 47
- Number of students who took both physics and chemistry = 5
- Number of students who took neither physics nor chemistry = 7
To find the total number of students surveyed, we can use the principle of Inclusion-Exclusion. According to this principle, the total number of students surveyed is equal to the sum of the students who took physics, the students who took chemistry, minus the students who took both, plus the students who took neither.
Total number of students surveyed = (Number of students who took physics) + (Number of students who took chemistry) - (Number of students who took both) + (Number of students who took neither)
Total number of students surveyed = 23 + 47 - 5 + 7
Calculating this expression will give us the answer to the question:
Total number of students surveyed = 72
Therefore, 72 recent high school grads were surveyed.