document.write( "Question 1017399: Rob has 40 coins, all dimes and quarters, worth $7.60. How many dimes and how many quarters does he have? \n" ); document.write( "

Algebra.Com's Answer #633692 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "Let the number of dimes be x\r\n" );
document.write( "Let the number of quarters 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( "dimes         x      $0.10     $0.10x\r\n" );
document.write( "quarters      y      $0.25     $0.25y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       40      -----     $7.60\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" );
document.write( "             \r\n" );
document.write( "                  x + y = 40\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( "          0.10x + 0.25y = 7.60\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( "              10x + 25y = 760\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 = 40\r\n" );
document.write( "                      y = 40 - x\r\n" );
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document.write( "Substitute (40 - x) for y in 10x + 25y = 760\r\n" );
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document.write( "       10x + 25(40 - x) = 760\r\n" );
document.write( "       10x + 1000 - 25x = 760\r\n" );
document.write( "            -15x + 1000 = 760\r\n" );
document.write( "                   -15x = -240\r\n" );
document.write( "                      x = 16 = the number of dimes.\r\n" );
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document.write( "        Substitute in y = 40 - x\r\n" );
document.write( "                      y = 40 - (16)\r\n" );
document.write( "                      y = 24 quarters.\r\n" );
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document.write( "Checking:  16 dimes is $1.60 and 24 quarters is $6.00\r\n" );
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document.write( "            That's 40 coins.\r\n" );
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document.write( "And indeed $1.60 + $6.00 = $7.60\r\n" );
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document.write( "Edwin

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