document.write( "Question 1026948: Alex has $3.65 in nickels and dimes. He has 45 coins.How many of each coin does he have? \n" ); document.write( "

Algebra.Com's Answer #642207 by Edwin McCravy(20081) $\"\"$ $\"About$

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document.write( "Let the number of nickels 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( "nickels       x      $0.05       $0.05x\r\n" );
document.write( "dimes         y      $0.10       $0.10y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       45      -----       $3.65\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 = 45\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( "           0.05x + 0.10y = 3.65\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 = 365\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 = 45\r\n" );
document.write( "                        y = 45 - x\r\n" );
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document.write( "Substitute (45 - x) for y in 5x + 10y = 365\r\n" );
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document.write( "          5x + 10(45 - x) = 365\r\n" );
document.write( "           5x + 450 - 10x = 365\r\n" );
document.write( "                -5x + 450 = 365\r\n" );
document.write( "                      -5x = -85\r\n" );
document.write( "                        x = 17 = the number of nickels.\r\n" );
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document.write( "          Substitute in y = 45 - x\r\n" );
document.write( "                        y = 45 - (17)\r\n" );
document.write( "                        y = 28 dimes.\r\n" );
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document.write( "Checking:  17 nickels is $0.85 and 28 dimes is $2.80\r\n" );
document.write( "            That's 45 coins.\r\n" );
document.write( "            And indeed $0.85 + $2.80 = $3.65\r\n" );
document.write( "Edwin

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