document.write( "Question 1033019: Kevin and Randy Muise have a jar containing 65 coins, all of which are either quarters and nickels. The total value of the coins in the jar is $13.05. How many of each type of coin do they have?
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Algebra.Com's Answer #647612 by Edwin McCravy(20059) $\"\"$ $\"About$

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document.write( "Let the number of quarters be x\r\n" );
document.write( "Let the number of nickels 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( "nickels       y      $0.05       $0.05y\r\n" );
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document.write( "TOTALS       65      -----      $13.05\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 = 65\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 + 0.05y = 13.05\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 + 5y = 1305\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 = 65\r\n" );
document.write( "               y = 65 - x\r\n" );
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document.write( "Substitute (65 - x) for y in 25x + 5y = 1305\r\n" );
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document.write( "    25x + 5(65 - x) = 1305\r\n" );
document.write( "     25x + 325 - 5x = 1305\r\n" );
document.write( "          20x + 325 = 1305\r\n" );
document.write( "                20x = 980\r\n" );
document.write( "                  x = 49 = the number of quarters.\r\n" );
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document.write( "Substitute in y = 65 - x\r\n" );
document.write( "              y = 65 - (49)\r\n" );
document.write( "              y = 16 nickels.\r\n" );
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document.write( "Checking:  49 quarters is $12.25 and 16 nickels is $0.80\r\n" );
document.write( "            That's 65 coins.\r\n" );
document.write( "            And indeed $12.25 + $0.80 = $13.05\r\n" );
document.write( "Edwin

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