document.write( "Question 174553: I have been stuck on this problem for a week now, Please help.\r
\n" ); document.write( "\n" ); document.write( "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?
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Algebra.Com's Answer #129561 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let him start out with \"x\" amount of rice
\n" ); document.write( "At the first he gives up 1/3 of his rice, so he has
\n" ); document.write( "\"%282%2F3%29%2Ax\" left
\n" ); document.write( "At the second he is allowed to keep 1/3 of what is left,
\n" ); document.write( "so now he has
\n" ); document.write( "\"%281%2F3%29%2A%282%2F3%29%2Ax\" left
\n" ); document.write( "At the third, he gives up 1/4 of what remains, so he gets to keep
\n" ); document.write( "3/4 of what remains. Now he has
\n" ); document.write( "\"%283%2F4%29%2A%281%2F3%29%2A%282%2F3%29%2Ax\"
\n" ); document.write( "After passing through all three customs stations, he has 6 pounds less than he started with, so he has \"x+-+6\"
\n" ); document.write( "\"x+-+6+=+%283%2F4%29%2A%281%2F3%29%2A%282%2F3%29%2Ax\"
\n" ); document.write( "\"x+-+6+=+%286%2F36%29%2Ax\"
\n" ); document.write( "\"x+-+6+=+%281%2F6%29%2Ax\"
\n" ); document.write( "multiply both sides by \"6\"
\n" ); document.write( "\"6x+-+36+=+x\"
\n" ); document.write( "\"5x+=+36\"
\n" ); document.write( "\"x+=+7.2\"
\n" ); document.write( "He had 7.2 pounds when he started
\n" ); document.write( "check:
\n" ); document.write( "\"%283%2F4%29%2A%281%2F3%29%2A%282%2F3%29%2A7.2+=+7.2+-+6\"
\n" ); document.write( "\"%281%2F6%29%2A7.2+=+1.2\"
\n" ); document.write( "\"1.2+=+1.2\"
\n" ); document.write( "OK
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