document.write( "Question 164168: $1.65 is made up of pennies, nickels, and dimes. Half of the coins are nickels. List a set of coins that will solve the problem including why only the set of coins you chose worked in this situation. Remember you are communication information to some one who may have no idea what you are talking about, so the more information you give, the better off you will be. Use proper grammar and complete sentences in your explanation \n" ); document.write( "
Algebra.Com's Answer #120966 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll just work the problem for you. You'll have to\r\n" );
document.write( "write it up using complete sentences and proper grammar,\r\n" );
document.write( "and filling in your own explanations.\r\n" );
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document.write( "Let p = the number of pennies\r\n" );
document.write( "Let n = the number of nickels\r\n" );
document.write( "Let d = the number of dimes\r\n" );
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document.write( "We have the equation:\r\n" );
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document.write( "\".01p+%2B+.05n+%2B+.10d+=+1.65\"\r\n" );
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document.write( "or multiplying through by 100,\r\n" );
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document.write( "\"p%2B5n%2B10d=165\"\r\n" );
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document.write( "Since half the coins are nickels, we have\r\n" );
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document.write( "\"n+=+%28p%2Bn%2Bd%29%2F2\"\r\n" );
document.write( "\r\n" );
document.write( "\"2n+=+p%2Bn%2Bd\"\r\n" );
document.write( "\r\n" );
document.write( "\"n=p%2Bd\" \r\n" );
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document.write( "We have the system:\r\n" );
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document.write( "\"system%28p+%2B+5n+%2B+10d+=+165%2Cn=p%2Bd%29\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting \"p%2Bd\" for \"n\" in the first equation\r\n" );
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document.write( "\"p+%2B+5%28p%2Bd%29+%2B+10d+=+165\"\r\n" );
document.write( "\r\n" );
document.write( "\"p+%2B+5p%2B5d+%2B+10d+=+165\"\r\n" );
document.write( "\r\n" );
document.write( "\"6p+%2B+15d+=+165\"\r\n" );
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document.write( "Divide through by 3:\r\n" );
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document.write( "\"2p+%2B+5d+=+55\"\r\n" );
document.write( "\r\n" );
document.write( "\"2p+=+55-5d\"\r\n" );
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document.write( "\"2p+=+5%2811-d%29\"\r\n" );
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document.write( "Since the left side is even,\r\n" );
document.write( "the right side must be even also,\r\n" );
document.write( "and positive. Therefore \"11-d\" \r\n" );
document.write( "must be even and positive, too, \r\n" );
document.write( "Therefore d must be odd and no more \r\n" );
document.write( "than 11.\r\n" );
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document.write( "Therefore there are 6 possibilities:\r\n" );
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document.write( "d = 1, 3, 5, 7, 9, or 11\r\n" );
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document.write( "If \"d=1\", then\r\n" );
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document.write( "\"2p+=+5%2811-d%29\" becomes\r\n" );
document.write( "\"2p+=+5%2811-1%29\"\r\n" );
document.write( "\"2p+=+5%2810%29\"\r\n" );
document.write( "\"2p+=+50\"\r\n" );
document.write( "\"p+=+25\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting \"d=1\" and \"p=25\"\r\n" );
document.write( "into\r\n" );
document.write( "\r\n" );
document.write( "\"p+%2B+5n+%2B+10d+=+165\"\r\n" );
document.write( "\"25+%2B+5n+%2B+10%281%29+=+165\"\r\n" );
document.write( "\"25+%2B+5n+%2B+10+=+165\"\r\n" );
document.write( "\"35+%2B+5n+=+165\"\r\n" );
document.write( "\"5n+=+130\"\r\n" );
document.write( "\"n+=+26\"\r\n" );
document.write( "\r\n" );
document.write( "So one possibility is \r\n" );
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document.write( "\"p=25\", \"n=26\", \"d=1\"\r\n" );
document.write( "\r\n" );
document.write( "-------\r\n" );
document.write( "\r\n" );
document.write( "If \"d=3\", then\r\n" );
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document.write( "\"2p+=+5%2811-d%29\" becomes\r\n" );
document.write( "\"2p+=+5%2811-3%29\"\r\n" );
document.write( "\"2p+=+5%288%29\"\r\n" );
document.write( "\"2p+=+40\"\r\n" );
document.write( "\"p+=+20\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting \"d=3\" and \"p=20\"\r\n" );
document.write( "into\r\n" );
document.write( "\r\n" );
document.write( "\"p+%2B+5n+%2B+10d+=+165\"\r\n" );
document.write( "\"20+%2B+5n+%2B+10%283%29+=+165\"\r\n" );
document.write( "\"20+%2B+5n+%2B+30+=+165\"\r\n" );
document.write( "\"50+%2B+5n+=+165\"\r\n" );
document.write( "\"5n+=+115\"\r\n" );
document.write( "\"n+=+23\"\r\n" );
document.write( "\r\n" );
document.write( "So another possibility is \r\n" );
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document.write( "\"p=20\", \"n=23\", \"d=3\"\r\n" );
document.write( "\r\n" );
document.write( "-----------------\r\n" );
document.write( "\r\n" );
document.write( "If \"d=5\", then\r\n" );
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document.write( "\"2p+=+5%2811-d%29\" becomes\r\n" );
document.write( "\"2p+=+5%2811-5%29\"\r\n" );
document.write( "\"2p+=+5%286%29\"\r\n" );
document.write( "\"2p+=+30\"\r\n" );
document.write( "\"p+=+15\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting \"d=5\" and \"p=15\"\r\n" );
document.write( "into\r\n" );
document.write( "\r\n" );
document.write( "\"p+%2B+5n+%2B+10d+=+165\"\r\n" );
document.write( "\"15+%2B+5n+%2B+10%285%29+=+165\"\r\n" );
document.write( "\"15+%2B+5n+%2B+50+=+165\"\r\n" );
document.write( "\"65+%2B+5n+=+165\"\r\n" );
document.write( "\"5n+=+100\"\r\n" );
document.write( "\"n+=+20\"\r\n" );
document.write( "\r\n" );
document.write( "So another possibility is \r\n" );
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document.write( "\"p=15\", \"n=20\", \"d=5\"\r\n" );
document.write( "\r\n" );
document.write( "-------------\r\n" );
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document.write( "If \"d=7\", then\r\n" );
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document.write( "\"2p+=+5%2811-d%29\" becomes\r\n" );
document.write( "\"2p+=+5%2811-7%29\"\r\n" );
document.write( "\"2p+=+5%284%29\"\r\n" );
document.write( "\"2p+=+20\"\r\n" );
document.write( "\"p+=+10\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting \"d=7\" and \"p=10\"\r\n" );
document.write( "into\r\n" );
document.write( "\r\n" );
document.write( "\"p+%2B+5n+%2B+10d+=+165\"\r\n" );
document.write( "\"10+%2B+5n+%2B+10%287%29+=+165\"\r\n" );
document.write( "\"10+%2B+5n+%2B+70+=+165\"\r\n" );
document.write( "\"80+%2B+5n+=+165\"\r\n" );
document.write( "\"5n+=+85\"\r\n" );
document.write( "\"n+=+17\"\r\n" );
document.write( "\r\n" );
document.write( "So another possibility is \r\n" );
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document.write( "\"p=10\", \"n=17\", \"d=7\"\r\n" );
document.write( "\r\n" );
document.write( "-------------\r\n" );
document.write( "\r\n" );
document.write( "If \"d=9\", then\r\n" );
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document.write( "\"2p+=+5%2811-d%29\" becomes\r\n" );
document.write( "\"2p+=+5%2811-9%29\"\r\n" );
document.write( "\"2p+=+5%282%29\"\r\n" );
document.write( "\"2p+=+10\"\r\n" );
document.write( "\"p+=+5\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting \"d=9\" and \"p=5\"\r\n" );
document.write( "into\r\n" );
document.write( "\r\n" );
document.write( "\"p+%2B+5n+%2B+10d+=+165\"\r\n" );
document.write( "\"5+%2B+5n+%2B+10%289%29+=+165\"\r\n" );
document.write( "\"5+%2B+5n+%2B+90+=+165\"\r\n" );
document.write( "\"95+%2B+5n+=+165\"\r\n" );
document.write( "\"5n+=+70\"\r\n" );
document.write( "\"n+=+14\"\r\n" );
document.write( "\r\n" );
document.write( "So another possibility is \r\n" );
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document.write( "\"p=5\", \"n=14\", \"d=9\"\r\n" );
document.write( "\r\n" );
document.write( "-------------\r\n" );
document.write( "\r\n" );
document.write( "If \"d=11\", then\r\n" );
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document.write( "\"2p+=+5%2811-d%29\" becomes\r\n" );
document.write( "\"2p+=+5%2811-11%29\"\r\n" );
document.write( "\"2p+=+5%280%29\"\r\n" );
document.write( "\"2p+=+0\"\r\n" );
document.write( "\"p+=+0\"\r\n" );
document.write( "\r\n" );
document.write( "Substituting \"d=11\" and \"p=0\"\r\n" );
document.write( "into\r\n" );
document.write( "\r\n" );
document.write( "\"p+%2B+5n+%2B+10d+=+165\"\r\n" );
document.write( "\"0+%2B+5n+%2B+10%2811%29+=+165\"\r\n" );
document.write( "\"0+%2B+5n+%2B+110+=+165\"\r\n" );
document.write( "\"5n+=+55\"\r\n" );
document.write( "\"n+=+11\"\r\n" );
document.write( "\r\n" );
document.write( "So another possibility is \r\n" );
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document.write( "\"p=0\", \"n=11\", \"d=11\"\r\n" );
document.write( "\r\n" );
document.write( "-------------\r\n" );
document.write( "\r\n" );
document.write( "So all the 6 possibilities are \r\n" );
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document.write( "0 pennies, 11 nickels, 11 dimes, 22 coins, half of which are 11 nickels.\r\n" );
document.write( "5 pennies, 14 nickels, 9 dimes, 28 coins, half of which are 14 nickels.\r\n" );
document.write( "10 pennies, 17 nickels, 7 dimes, 34 coins, half of which are 17 nickels.\r\n" );
document.write( "15 pennies, 20 nickels, 5 dimes, 40 coins, half of which are 20 nickels.\r\n" );
document.write( "20 pennies, 23 nickels, 3 dimes, 46 coins, half of which are 23 nickels.\r\n" );
document.write( "25 pennies, 26 nickels, 1 dimes, 52 coins, half of which are 26 nickels.\r\n" );
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document.write( "Edwin
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