document.write( "Question 1028601: A jar has quarter and nickels with 76 coins. Total value is 10.80. Find the amount quarter and nickels \n" ); document.write( "

Algebra.Com's Answer #643690 by Edwin McCravy(20081) $\"\"$ $\"About$

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document.write( "Let the number of quarters be x\r\n" );
document.write( "Let the number of nickels 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( "quarters      x       $0.25      $0.25x\r\n" );
document.write( "nickels       y       $0.05      $0.05y\r\n" );
document.write( "-------------------------------------------\r\n" );
document.write( "TOTALS       76       -----     $10.80\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 = 76\r\n" );
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document.write( " The second equation comes from the last column.\r\n" );
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document.write( "         0.25x + 0.05y = 10.8\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( "          25x + 5y = 1080\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 = 76\r\n" );
document.write( "               y = 76 - x\r\n" );
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document.write( "Substitute (76 - x) for y in 25x + 5y = 1080\r\n" );
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document.write( "    25x + 5(76 - x) = 1080\r\n" );
document.write( "     25x + 380 - 5x = 1080\r\n" );
document.write( "          20x + 380 = 1080\r\n" );
document.write( "                20x = 700\r\n" );
document.write( "                  x = 35 = the number of quarters.\r\n" );
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document.write( "Substitute in y = 76 - x\r\n" );
document.write( "              y = 76 - (35)\r\n" );
document.write( "              y = 41 nickels.\r\n" );
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document.write( "Checking:  35 quarters is $8.75 and 41 nickels is $2.05\r\n" );
document.write( "            That's 76 coins.\r\n" );
document.write( "            And indeed $8.75 + $2.05 = $10.80\r\n" );
document.write( "Edwin

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