document.write( "Question 1031132: Gabby's piggy bank contains nickles and dimes worth $4.05. If she has 59 coins in all, how many of each does she have? \n" ); document.write( "

Algebra.Com's Answer #645870 by Edwin McCravy(20059) $\"\"$ $\"About$

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document.write( "Let the number of nickles 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" );
document.write( "-------------------------------------------\r\n" );
document.write( "nickles      x      $0.05       $0.05x\r\n" );
document.write( "dimes        y      $0.10       $0.10y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS      59      -----       $4.05\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 = 59\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
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document.write( "           0.05x + 0.10y = 4.05\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( "                5x + 10y = 405\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 = 59\r\n" );
document.write( "                       y = 59 - x\r\n" );
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document.write( "Substitute (59 - x) for y in 5x + 10y = 405\r\n" );
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document.write( "         5x + 10(59 - x) = 405\r\n" );
document.write( "          5x + 590 - 10x = 405\r\n" );
document.write( "               -5x + 590 = 405\r\n" );
document.write( "                     -5x = -185\r\n" );
document.write( "                       x = 37 = the number of nickles.\r\n" );
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document.write( "Substitute in          y = 59 - x\r\n" );
document.write( "                       y = 59 - (37)\r\n" );
document.write( "                       y = 22 dimes.\r\n" );
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document.write( "Checking:  37 nickles is $1.85 and 22 dimes is $2.20\r\n" );
document.write( "           That's 59 coins.\r\n" );
document.write( "           And indeed $1.85 + $2.20 = $4.05\r\n" );
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document.write( "Edwin

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