SOLUTION: At the local coffee shop, 80% of students purchase coffee because they need caffeine, 30% purchase a muffin because they are hungry and 24% purchase both a muffin and a coffee. Wha

Question 1040313: At the local coffee shop, 80% of students purchase coffee because they need caffeine, 30% purchase a muffin because they are hungry and 24% purchase both a muffin and a coffee. What percentage of students:
a. Purchase either a coffee or a muffin or both?
b. Do not purchase either?
c. Purchase only a coffee but not a muffin?
d. Purchase only a muffin but not a coffee?
e. Purchase either but not both?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
At the local coffee shop, 80% of students purchase coffee because they need caffeine, 30% purchase a muffin because they are hungry and 24% purchase both a muffin and a coffee. What percentage of students:
Sketch 2 intersecting cirecles
The intersecting section is 24%
The remaining section of the muffin circle is 30-24 = 6%
The remaining section of the coffee circle is 80-24 = 56%
The section outside both circles is 100-(6+24+56) = 14%
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a. Purchase either a coffee or a muffin or both?:: 86%
b. Do not purchase either?:: 14%
c. Purchase only a coffee but not a muffin?::56%
d. Purchase only a muffin but not a coffee?:: 6%
e. Purchase either but not both?::6+56 = 62%
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Cheers,
Stan H.
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