Question 395155: three travelers arrived tired ang hungry at a lonely inn.the innkeeper apologized and said he could only offer them a meal of potatoes. When he brought in the dish, all men were sleep. after a while , one of the three woke up, ate a third of the potatoes, ang went back sleep. soon afterward another woke up, ate a third of the potatoes that remained, and promptly fell asleep again. then the third man did likewas. when the innkeeper came back, he found 8 potatoes were left. how many had he put on the dish.??
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! three travelers arrived tired ang hungry at a lonely inn.the innkeeper apologized and said he could only offer them a meal of potatoes. When he brought in the dish, all men were sleep. after a while , one of the three woke up, ate a third of the potatoes, ang went back sleep. soon afterward another woke up, ate a third of the potatoes that remained, and promptly fell asleep again. then the third man did likewas. when the innkeeper came back, he found 8 potatoes were left. how many had he put on the dish.??
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let the total potatoes be x
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First ate 1/3
Balance = x-x/3 = 2x/3.
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second ate 1/3 of 2x/3 = 2x/9
so balance was 2x/3 -2x/9 = (12x-4x)/18=8x/18 = 4x/9
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Third ate 1/3 of 4x/9 = 4x/27
so balance = 4x/9 -4x/27 = 8
(12x-4x)/27 =8
8x=27*8
/8
x= 27 potatoes were put in the dish.
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