document.write( "Question 992200: Ron has 11 coins with a total value of $1.55. The coins are nickels and quarters. How many of each coin does he have? \n" ); document.write( "
Algebra.Com's Answer #611831 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You can either do it with 1 unknown or with 2 unknowns.\r\n" );
document.write( "I'll do it both ways.\r\n" );
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document.write( "With 1 unknown\r\n" );
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document.write( "Let the number of nickels be x\r\n" );
document.write( "Then the number of quarters, using\r\n" );
document.write( "ONE PART = TOTAL MINUS OTHER PART,\r\n" );
document.write( "is 11-x.\r\n" );
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" );
document.write( "-------------------------------------------\r\n" );
document.write( "nickels      x        $0.05    $0.05x\r\n" );
document.write( "quarters   11-x       $0.25    $0.25(11-x)\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS      11        -----    $1.55\r\n" );
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document.write( " The equation comes from the column on the right\r\n" );
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document.write( "  \"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickels%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29\"\"%22%22=%22%22\"\"%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29\"\r\n" );
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document.write( "        0.05x + 0.25(11-x) = 1.55\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( "             5x + 25(11-x) = 155\r\n" );
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document.write( "            5x + 275 - 25x = 155\r\n" );
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document.write( "                -20x + 275 = 155\r\n" );
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document.write( "                      -20x = -120\r\n" );
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document.write( "                         x = 6 = the number of nickels.\r\n" );
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document.write( "The number of quarters is 11-x or 11-6 or 5 quarters.\r\n" );
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document.write( "Checking:  6 nickels is $0.30 and 5 quarters is $1.25\r\n" );
document.write( "            That's 11 coins.\r\n" );
document.write( "            And indeed $0.30 + $1.25 = $1.55\r\n" );
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document.write( "---------------------\r\n" );
document.write( "With two unknowns\r\n" );
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document.write( "Let the number of nickels be x\r\n" );
document.write( "Let the number of quarters 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" );
document.write( "-------------------------------------------\r\n" );
document.write( "nickels       x      $0.05     $0.05x\r\n" );
document.write( "quarters      y      $0.25     $0.25y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       11      -----     $1.55\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%2Cnickels%29%29\"\"%22%22%2B%22%22\"\"%28matrix%283%2C1%2CNumber%2Cof%2Cquarters%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 = 11\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%2Cnickels%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29\"\"%22%22=%22%22\"\"%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29\"\r\n" );
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document.write( "           0.05x + 0.25y = 1.55\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( "                5x + 25y = 155\r\n" );
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document.write( " So we have the system of equations:\r\n" );
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document.write( "           \"system%28x+%2B+y+=+11%2C5x+%2B+25y+=+155%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 = 11\r\n" );
document.write( "               y = 11 - x\r\n" );
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document.write( "Substitute (11 - x) for y in 5x + 25y = 155\r\n" );
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document.write( "  5x + 25(11 - x) = 155\r\n" );
document.write( "   5x + 275 - 25x = 155\r\n" );
document.write( "       -20x + 275 = 155\r\n" );
document.write( "             -20x = -120\r\n" );
document.write( "                x = 6 = the number of nickels.\r\n" );
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document.write( "Substitute in y = 11 - x\r\n" );
document.write( "              y = 11 - (6\r\n" );
document.write( "              y = 5 quarters.\r\n" );
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document.write( "The number of quarters is 11-x or 11-6 or 5 quarters.\r\n" );
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document.write( "Checking:  6 nickels is $0.30 and 5 quarters is $1.25\r\n" );
document.write( "            That's 11 coins.\r\n" );
document.write( "            And indeed $0.30 + $1.25 = $1.55dwin
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