The questions are:
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<span><span>
<span>
<span>How many students are not taking any science, math, or
English? AND
How many students are taking exactly one of science, math, or English
classes?</span>
</span>
</span>
</span></span>
This is best answered using a Venn diagram. If you look at
the separate areas, you see there are 7 areas.
The common area is the two students who takes the three
classes.
4 said they were taking both math and English
4 – 2 = 2 only take math & English
7 said they were taking both science and math
7 – 2 = 5 only take math and science
10 said they were taking both science and English
10 – 2 = 8 only take science and English
17 said they were taking English
17 – (2 + 8 + 2) = 5 take only English
22 said they were taking math
22 – (2 + 5 + 2) = 13 take math
24 said they were taking science
24 – (2 + 8 + 5) = 9 only take science
Adding them all up:
2 + 9 + 13 + 5 + 8 + 5 + 2 = 44
So, 44 students are taking the 3 courses
53 – 44 = 9 students are not taking any of the 3 courses
5 + 13 + 9 = 27 take only 1 of these courses
