document.write( "Question 1034899: angelina has collection of nickels and dimes worth &4.65. if she has 70 nickels and dimes, how many of each does she have? \n" ); document.write( "

Algebra.Com's Answer #649542 by Edwin McCravy(20056) $\"\"$ $\"About$

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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" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS      70      -----       $4.65\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 = 70\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 = 4.65\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 = 465\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 = 70\r\n" );
document.write( "                      y = 70 - x\r\n" );
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document.write( "Substitute (70 - x) for y in 5x + 10y = 465\r\n" );
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document.write( "        5x + 10(70 - x) = 465\r\n" );
document.write( "         5x + 700 - 10x = 465\r\n" );
document.write( "              -5x + 700 = 465\r\n" );
document.write( "                    -5x = -235\r\n" );
document.write( "                 x = 47 = the number of nickels.\r\n" );
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document.write( "Substitute in y = 70 - x\r\n" );
document.write( "              y = 70 - (47)\r\n" );
document.write( "              y = 23 dimes.\r\n" );
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document.write( "Checking:  47 nickels is $2.35 and 23 dimes is $2.30\r\n" );
document.write( "            That's 70 coins.\r\n" );
document.write( "            And indeed $2.35 + $2.30 = $4.65\r\n" );
document.write( "Edwin

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