document.write( "Question 1027510: In a childs bank are 17 coins that have a value of $3.50 the coins are either quarters or dimes how many coins each does child have?
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Algebra.Com's Answer #642718 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       17      -----        $3.50\r\n" );
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document.write( "The first equation comes from the \"Number of coins\" \r\n" );
document.write( "column.\r\n" );
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document.write( "  \r\n" );
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document.write( "                 x + y = 17\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 = 3.50\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 = 350\r\n" );
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document.write( " So we have the system of equations:\r\n" );
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 = 17\r\n" );
document.write( "                       y = 17 - x\r\n" );
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document.write( "Substitute (17 - x) for y in 25x + 10y = 350\r\n" );
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document.write( "        25x + 10(17 - x) = 350\r\n" );
document.write( "         25x + 170 - 10x = 350\r\n" );
document.write( "               15x + 170 = 350\r\n" );
document.write( "                     15x = 180\r\n" );
document.write( "                       x = 12 = the number of quarters.\r\n" );
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document.write( "Substitute in y = 17 - x\r\n" );
document.write( "              y = 17 - (12)\r\n" );
document.write( "              y = 5 dimes.\r\n" );
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document.write( "Checking:  12 quarters is $3.00 and 5 dimes is $0.50\r\n" );
document.write( "            That's 17 coins.\r\n" );
document.write( "            And indeed $3.00 + $0.50 = $3.50\r\n" );
document.write( "Edwin

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