SOLUTION: I have been stuck on this problem for a week now, Please help. A man is carrying rice on a journey. He passes through three custom stations. At the first he gives up 1/3 of his

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Question 174553: I have been stuck on this problem for a week now, Please help.
A man is carrying rice on a journey. He passes through three custom stations. At the first he gives up 1/3 of his rice; at the second he is allowed to keep 1/3 of what is left; and at the third, he gives up 1/4 of what remains. After passing through all three customs stations, he has 6 pounds less than he started with. How much rice did he have when he started?
Answer by josmiceli(6796) About Me  (Show Source):
You can put this solution on YOUR website!
Let him start out with x amount of rice
At the first he gives up 1/3 of his rice, so he has
%282%2F3%29%2Ax left
At the second he is allowed to keep 1/3 of what is left,
so now he has
%281%2F3%29%2A%282%2F3%29%2Ax left
At the third, he gives up 1/4 of what remains, so he gets to keep
3/4 of what remains. Now he has
%283%2F4%29%2A%281%2F3%29%2A%282%2F3%29%2Ax
After passing through all three customs stations, he has 6 pounds less than he started with, so he has x+-+6
x+-+6+=+%283%2F4%29%2A%281%2F3%29%2A%282%2F3%29%2Ax
x+-+6+=+%286%2F36%29%2Ax
x+-+6+=+%281%2F6%29%2Ax
multiply both sides by 6
6x+-+36+=+x
5x+=+36
x+=+7.2
He had 7.2 pounds when he started
check:
%283%2F4%29%2A%281%2F3%29%2A%282%2F3%29%2A7.2+=+7.2+-+6
%281%2F6%29%2A7.2+=+1.2
1.2+=+1.2
OK