Miss Sundaram wrote:60 people are asked to rank three ice cream flavors - Chocolate, Strawberry and Vanilla. No single person provides the same rank to two individuals.
36 people ranked vanilla third.
10% of the people surveyed ranked vanilla above strawberry
30% of the people surveyed ranked vanilla above chocolate
How many of the people surveyed ranked vanilla first?
Let V = vanilla, C = chocolate, and S = strawberry.
VCS = vanilla ranked first, chocolate ranked second, and strawberry ranked third.
VSC = vanilla ranked first, strawberry ranked second, and chocolate ranked third.
We are asked to determine how many people ranked vanilla first.
In other words:
VCS + VSC.
The sum of all of the rankings is 60:
VCS + VSC + CVS + CSV + SCV + SVC = 60.
36 people ranked vanilla third:
CSV + SCV = 36.
Thus, the sum of the remaining rankings is 24:
VCS + VSC + CVS + SVC = 24.
10% of the people surveyed ranked vanilla above strawberry:
VCS + VSC+ CVS = 6.
Subtracting the 2 equations directly above, we get:
(VCS + VSC + CVS + SVC) - (VCS + VSC+ CVS) = 24-6
SVC = 18.
30% of the people surveyed ranked vanilla above chocolate:
VCS + VSC + SVC = 18.
Since SVC = 18, VCS + VSC = 0.
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