document.write( "Question 1035410: Kevin and Randy Muise have a jar containing
\n" ); document.write( "28 coins, all of which are either quarters or nickels.
\n" ); document.write( "The total value of the coins in the jar is 4.00.
\n" ); document.write( "How many of each type of coin do they have? \n" ); document.write( "
Algebra.Com's Answer #650056 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
Kevin and Randy Muise have a jar containing
\n" ); document.write( "28 coins, all of which are either quarters or nickels.
\n" ); document.write( "The total value of the coins in the jar is $4.00.
\n" ); document.write( "How many of each type of coin do they have?
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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" );
document.write( "-------------------------------------------\r\n" );
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       28      -----       $4.00\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( "  \"%28matrix%283%2C1%2CNumber%2Cof%2Cquarters%29%29\"\"%22%22%2B%22%22\"\"%28matrix%283%2C1%2CNumber%2Cof%2Cnickels%29%29\"\"%22%22=%22%22\"\"%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccoins%29%29\"\r\n" );
document.write( "                 x + y = 28\r\n" );
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document.write( " The second equation comes from the \"Value of all coins\" column.\r\n" );
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document.write( "  \"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29\"\"%22%22%2B%22%22\"\"%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickels%29%29\"\"%22%22=%22%22\"\"%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29\"\r\n" );
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document.write( "           0.25x + 0.05y = 4\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 = 400\r\n" );
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document.write( " So we have the system of equations:\r\n" );
document.write( "           \"system%28x+%2B+y+=+28%2C25x+%2B+5y+=+400%29\".\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 = 28\r\n" );
document.write( "               y = 28 - x\r\n" );
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document.write( "Substitute (28 - x) for y in 25x + 5y = 400\r\n" );
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document.write( "    25x + 5(28 - x) = 400\r\n" );
document.write( "     25x + 140 - 5x = 400\r\n" );
document.write( "          20x + 140 = 400\r\n" );
document.write( "                20x = 260\r\n" );
document.write( "                  x = 13 = the number of quarters.\r\n" );
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document.write( "Substitute in y = 28 - x\r\n" );
document.write( "              y = 28 - (13)\r\n" );
document.write( "              y = 15 nickels.\r\n" );
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document.write( "Checking:  13 quarters is $3.25 and 15 nickels is $0.75\r\n" );
document.write( "            That's 28 coins.\r\n" );
document.write( "            And indeed $3.25 + $0.75 = $4.00\r\n" );
document.write( "Edwin

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