The third-place finisher of the Allen County hot dog eating contest, in which each contestant was given an equal amount of time to eat as many hot dogs as possible, required an average of 15 seconds to consume each hot dog. How many hot dogs did the winner eat?
(1) The winner consumed 24 more hot dogs than did the third-place finisher.
(2) The winner consumed hot dogs at double the rate of the third-place finisher.
and c
Let W = the number of hot dogs consumed by the winner.
Let T = the number of hot dogs consumed by the third-place finisher.
Statement 1: The winner consumed 24 more hot dogs than did the third-place finisher.
W = T + 24.
No way to solve for W.
INSUFFICIENT.
Statement 2: The winner consumed hot dogs at double the rate of the third-place finisher.
Since the winner ate twice as fast, he consumed TWICE the number of hot dogs:
W = 2T.
No way to solve for W.
INSUFFICIENT.
Statement combined:
Since we have two variables and two distinct linear equations, we can solve for each variable.
SUFFICIENT.
The correct answer is
C.
The rate given for the third-place finisher -- 15 seconds per hot dog -- is irrelevant.
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