document.write( "Question 1025173: If Cesar has 17 nickels and quarters in his pocket, and they have a combined value of 265 cents, how many of each coin does he have ? \n" ); document.write( "

Algebra.Com's Answer #640503 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 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( "nickels        x      $0.05       $0.05x\r\n" );
document.write( "quarters       y      $0.25       $0.25y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS        17      -----       $2.65\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 = 17\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 + 0.25y = 2.65\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 + 25y = 265\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 = 17\r\n" );
document.write( "               y = 17 - x\r\n" );
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document.write( "Substitute (17 - x) for y in 5x + 25y = 265\r\n" );
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document.write( "     5x + 25(17 - x) = 265\r\n" );
document.write( "      5x + 425 - 25x = 265\r\n" );
document.write( "          -20x + 425 = 265\r\n" );
document.write( "                -20x = -160\r\n" );
document.write( "                   x = 8 = the number of nickels.\r\n" );
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document.write( "Substitute in y = 17 - x\r\n" );
document.write( "              y = 17 - (8\r\n" );
document.write( "              y = 9 quarters.\r\n" );
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document.write( "Checking:  8 nickels is $0.40 and 9 quarters is $2.25\r\n" );
document.write( "            That's 17 coins.\r\n" );
document.write( "            And indeed $0.40 + $2.25 = $2.65\r\n" );
document.write( "Edwin

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