SOLUTION: 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; at

Question 184330: 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; at the second he is allowed to keep 1/3 of what is left; and at the third. 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?
I have been struggling with this problem for over a week now and still can't even figure out where to start. Thanks for the help
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let x=starting amount

"At the first he gives up 1/3 of his rice" ___ x-(1/3)x=(2/3)x remaining

"at the second he is allowed to keep 1/3 of what is left" ___ (1/3)*(2x/3)=2x/9 remaining

"at the third, he gives up 1/4 of what remains" ___ (2x/9)-(1/4)*(2x/9)=x/6 remaining

"After passing through all three customs stations, he has 6 pounds less than he started with"
___ x/6 = x-6

multiplying by 6 ___ x=6x-36

adding 36-x ___ 36=5x

dividing by 5 ___ 7.2=x

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