document.write( "Question 1023819: A collection of 100 coins consist of 5 and 10 if the total value is 725 find the number of coins of each denomination \n" ); document.write( "

Algebra.Com's Answer #639310 by Edwin McCravy(20060) $\"\"$ $\"About$

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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" );
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document.write( "nickels      x        $0.05      $0.05x\r\n" );
document.write( "dimes        y        $0.10      $0.10y\r\n" );
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document.write( "TOTALS       100      -----      $7.25\r\n" );
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document.write( " The first equation comes from the second column.\r\n" );
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document.write( "  \r\n" );
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document.write( "                 x + y = 100\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 = 7.25\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( "              5x + 10y = 725\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 = 100\r\n" );
document.write( "               y = 100 - x\r\n" );
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document.write( "Substitute (100 - x) for y in 5x + 10y = 725\r\n" );
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document.write( "    5x + 10(100 - x) = 725\r\n" );
document.write( "     5x + 1000 - 10x = 725\r\n" );
document.write( "          -5x + 1000 = 725\r\n" );
document.write( "                 -5x = -275\r\n" );
document.write( "                   x = 55 = the number of nickels.\r\n" );
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document.write( "Substitute in y = 100 - x\r\n" );
document.write( "              y = 100 - (55\r\n" );
document.write( "              y = 45 dimes.\r\n" );
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document.write( "Checking:  55 nickels is $2.75 and 45 dimes is $4.50\r\n" );
document.write( "            That's 100 coins.\r\n" );
document.write( "            And indeed $2.75 + $4.50 = $7.25\r\n" );
document.write( "Edwin

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