Math problem for the genius
[From: ] [author: ] [Date: 11-11-27] [Hit: ]
after all three eat, there are (2/3)^3 of the original portion of potatoes left, OR...x*(2/3)^3 = x*(8/27)and from the problem statement,......
To solve this multiply by 3*3*3, which gives 2*2*2x = 8*27
Now divide by 2*2*2, which gives x = 27
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There's a much easier way to do this.
So there's x number of potatoes.
The first person eats 1/3 of that, so there's 2/3 left, and the other two do the same. So basically, after all three eat, there are (2/3)^3 of the original portion of potatoes left, OR...
x*(2/3)^3 = x*(8/27)
and from the problem statement, we know...
x*(8/27) = 8
x = 27
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The number of potatoes the inn keeper gave the men is x.
The first man ate x/3 potatoes.
The second man ate (x/3)/3
The third man ate ((x/3)/3)/3) potatoes.
x - (x/3) - (x/3)/3 - ((x/3)/3)/3) = 8
x - x/3 - x/9 - x/27 = 8
x(1-1/3-1/9-1/27) = 8
x(27/27 - 9/27 -3/27 - 1/27) = 8
14x/27 = 8
14x = 378
x = 378/14
x = 27 potatoes
hope this helps.
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27 potatoes
remember 8 is 2/3 part of the remaining potatoes(1/3 is taken)
(2/3)x = 8, then x = 12,
(2/3)x = 12, then x = 18
(2/3)x = 18, then x = 27
I used reverse math. :)
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Let X = total number of potatoes
The first traveler eats X/3
The second traveler eats 1/3(2X/3) = 2X/9
The third guy eats 1/3(X-X/3 - 2X/9) = 4X/27
So 8 = X - X/3 - 2X/9 - 4X/27
So X = 27
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Simply multiply eight by 3, for each time a man ate a third.
So it'd be...
8 * 3 * 3 * 3
Or 8*3^3
And your answer will be 216.
To check your work multiply by 1/3 for each man and you will get 8.
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27 potatoes.
