document.write( "Question 1009623: a change purse contains only quarters and dimes. There are 15 coins in the purse. the value of the coins is $2.70. determine the number of quarters and dimes in the purse. \n" ); document.write( "
Algebra.Com's Answer #625097 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Let the number of quarters be x\r\n" );
document.write( "Let the number of dimes be y\r\n" );
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document.write( "                      Value      Value\r\n" );
document.write( "Type       Number       of         of\r\n" );
document.write( " of          of        EACH       ALL\r\n" );
document.write( "coin        coins      coin      coins\r\n" );
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document.write( "quarters      x      $0.25     $0.25x\r\n" );
document.write( "dimes         y      $0.10     $0.10y\r\n" );
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document.write( "TOTALS       15      -----     $2.70\r\n" );
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document.write( " The first equation comes from the second column.\r\n" );
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document.write( "  \"%28matrix%283%2C1%2CNumber%2Cof%2Cquarters%29%29\"\"%22%22%2B%22%22\"\"%28matrix%283%2C1%2CNumber%2Cof%2Cdimes%29%29\"\"%22%22=%22%22\"\"%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccoins%29%29\"\r\n" );
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document.write( "                   x + y = 15\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
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document.write( "  \"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cdimes%29%29\"\"%22%22=%22%22\"\"%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29\"\r\n" );
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document.write( "           0.25x + 0.10y = 2.70\r\n" );
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document.write( "Get rid of decimals by multiplying every term by 100:\r\n" );
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document.write( "               25x + 10y = 270\r\n" );
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document.write( " So we have the system of equations:\r\n" );
document.write( "           \"system%28x+%2B+y+=+15%2C25x+%2B+10y+=+270%29\".\r\n" );
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document.write( "We solve by substitution.  Solve the first equation for y:\r\n" );
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document.write( "                   x + y = 15\r\n" );
document.write( "                       y = 15 - x\r\n" );
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document.write( "Substitute (15 - x) for y in 25x + 10y = 270\r\n" );
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document.write( "        25x + 10(15 - x) = 270\r\n" );
document.write( "         25x + 150 - 10x = 270\r\n" );
document.write( "               15x + 150 = 270\r\n" );
document.write( "                     15x = 120\r\n" );
document.write( "                       x = 8 = the number of quarters.\r\n" );
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document.write( "Substitute in y = 15 - x\r\n" );
document.write( "              y = 15 - (8)\r\n" );
document.write( "              y = 7 dimes.\r\n" );
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document.write( "Checking:  8 quarters is $2.00 and 7 dimes is $0.70\r\n" );
document.write( "            That's 15 coins.\r\n" );
document.write( "            And indeed $2.00 + $0.70 = $2.70\r\n" );
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document.write( "Edwin
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