document.write( "Question 57413: You are given exactly one thousand dollars in in one-dollar bills. You are also given exactly ten envelopes. Your task is to place the dollar bills in the envelopes so that you can dispense any amount of money from $1 to $1,000 by using a combination of the envelopes. \n" ); document.write( "
Algebra.Com's Answer #39170 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Try an easier problem first.
\n" ); document.write( "What if I had 5 envelopes to put $31 dollar bills in so I could
\n" ); document.write( "come up with any amount?
\n" ); document.write( "I could fill the enveolpes like this
\n" ); document.write( "$1, $2, $4, $8, $16
\n" ); document.write( "Check and see if there's any amount that you can't get with combinations
\n" ); document.write( "of envelopes. There isn't.
\n" ); document.write( "What if I had $27 instead of $31?
\n" ); document.write( "I'd fill them like this
\n" ); document.write( "$1, $2, $4, $8, $12
\n" ); document.write( "It still works
\n" ); document.write( "Now how to fill 10 envelopes with $1 bills so I can get any amount up to
\n" ); document.write( "$1000
\n" ); document.write( "Well, If I fill them this way,
\n" ); document.write( "$1, $2, $4, $8, $16, $32, $64, $128, $256, $512
\n" ); document.write( "Each number is double the previous one, but I use up more than my $1000
\n" ); document.write( "1+ 2+ 4+ 8+ 16+ 32+ 64+ 128+ 256+ 512 = 1023
\n" ); document.write( "So I need to subtract $23 from the $512. That makes $489 that I
\n" ); document.write( "need to put in the last envelope.
\n" ); document.write( "$1, $2, $4, $8, $16, $32, $64, $128, $256, $489 is the answer \n" ); document.write( "
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