Question 1189422: An empty fuel tank is filled with brand Z gasoline. When the tank is half empty, it is filled with brand Y gasoline. When the tank is half empty again, it is filled with brand Z gasoline. When the tank is half empty again, it is filled with brand Y gasoline. At this time, what percent of the gasoline in the tank is brand Z?
Answer by ikleyn(52908)   (Show Source):
You can put this solution on YOUR website! .
(1) An empty fuel tank is filled with brand Z gasoline.
(2) When the tank is half empty, it is filled with brand Y gasoline.
(3) When the tank is half empty again, it is filled with brand Z gasoline.
(4) When the tank is half empty again, it is filled with brand Y gasoline.
At this time, what percent of the gasoline in the tank is brand Z?
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I edited the post by placing numbers for each step, in order for easy refer to these steps.
After step (1), we have the full tank of gasoline (Z).
After step (2), we have the full step of gasoline (Z/2,Y/2).
After step (3), we have full tank of gasoline (Z/4+Z/2,Y/4) = {3Z/4,Y/4).
After step (4), we have full tank of gasoline (3Z/8,Y/8+Y/2) = (3Z/8,5Y/8)
ANSWER. After step (4), we have 3Z/8 brand Z in the tank, which is  = 37.5% of gasoline Z of the tank volume.
Solved.
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