Four men were shipwrecked on an island. Having no food, they went to work gathering pineapples. After gathering pineapples, they were tired and all fell asleep. After another while, one of the men awoke and was very hungry so he ate 1/3 of the pineapples - more than his proper share. He then went back to sleep. The second man awoke and being hungry, ate 1/3 of the remaining pineapples and went back to sleep. The third man did the same. When the fourth man awoke, he took only his rightful share of the remaining pineapples. Then there were 6 pineapples left. How many pineapples did the men gather?

2 answers

They gathered "x" pineapples

Guy 1 ate (1/3)x = x/3 ----> 2/3 remain
Guy 2 ate (1/3)(2/3)x = 2x/9 ----> 4/9 remain
Guy 3 ate (1/3)(4/9)x = 4x/27 ----> 8/27 remain
Guy 4 ate (1/4)(8/27)x = 2x/27 ----> 6 remain

(x/3) + (2x/9) + (4x/27) + (2x/27) + 6 = x
9x + 6x + 4x + 2x + 162 = 27x
21x + 162 = 27x
6x = 162
x = 27
how did you get the 4x/27?
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