document.write( "Question 984189: 29 coins all nickels and quarters in a jar sum if the coins is 4 dollars and 45 cents. how many of each coin is there? \n" ); document.write( "
Algebra.Com's Answer #604961 by AnlytcPhil(1807)\"\" \"About 
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document.write( "The above solution uses only 1 unknown.  It can also be solved\r\n" );
document.write( "using 2 unknowns.  The following uses 2 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" );
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( "nickels       x       $0.05     $0.05x\r\n" );
document.write( "quarters      y       $0.25     $0.25y\r\n" );
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document.write( "TOTALS       29       -----     $4.45\r\n" );
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document.write( " The first equation comes from the \"number of coins\" 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 = 29\r\n" );
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document.write( " The second equation comes from the \"VALUE of all coins\" 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 = 4.45\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 = 445\r\n" );
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document.write( " So we have the system of equations:\r\n" );
document.write( "\"system%28x+%2B+y+=+29%2C5x+%2B+25y+=+445%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 = 29\r\n" );
document.write( "      y = 29 - x\r\n" );
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document.write( "Substitute (29 - x) for y in 5x + 25y = 445\r\n" );
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document.write( "     5x + 25(29 - x) = 445\r\n" );
document.write( "      5x + 725 - 25x = 445\r\n" );
document.write( "          -20x + 725 = 445\r\n" );
document.write( "                -20x = -280\r\n" );
document.write( "                   x = 14 = the number of nickels.\r\n" );
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document.write( "     Substitute in y = 29 - x\r\n" );
document.write( "                   y = 29 - 14\r\n" );
document.write( "                   y = 15 quarters.\r\n" );
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document.write( "The number of quarters is 29-x or 29-14 or 15 quarters.\r\n" );
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document.write( "Checking:  14 nickels is $0.70 and 15 quarters is $3.75\r\n" );
document.write( "            That's 29 coins.\r\n" );
document.write( "            And indeed $0.70 + $3.70 = $4.45\r\n" );
document.write( "Edwin

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