document.write( "Question 1032067: There are 32 quarters and dimes in a jar. The total amount
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Algebra.Com's Answer #646783 by Edwin McCravy(20065) $\"\"$ $\"About$

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There are 32 quarters and dimes in a jar. The total amount
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document.write( "There can be no solution with 32 coins.\r\n" );
document.write( "Perhaps you meant 33 coins instead.  I will\r\n" );
document.write( "assume so.\r\n" );
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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      33      -----       $5.25\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( "  \r\n" );
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document.write( "                 x + y = 33\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
document.write( "  \r\n" );
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document.write( "         0.25x + 0.10y = 5.25\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 = 525\r\n" );
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document.write( " So we have the system of equations:\r\n" );
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document.write( "           .\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 = 33\r\n" );
document.write( "               y = 33 - x\r\n" );
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document.write( "Substitute (33 - x) for y in 25x + 10y = 525\r\n" );
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document.write( "   25x + 10(33 - x) = 525\r\n" );
document.write( "    25x + 330 - 10x = 525\r\n" );
document.write( "          15x + 330 = 525\r\n" );
document.write( "                15x = 195\r\n" );
document.write( "                  x = 13 = the number of quarters.\r\n" );
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document.write( "Substitute in y = 33 - x\r\n" );
document.write( "              y = 33 - (13\r\n" );
document.write( "              y = 20 dimes.\r\n" );
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document.write( "Checking:  13 quarters is $3.25 and 20 dimes is $2.00\r\n" );
document.write( "            That's 33 coins.\r\n" );
document.write( "            And indeed $3.25 + $2.00 = $5.25\r\n" );
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document.write( "Edwin \n" );
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