document.write( "Question 1049416: I don't understand how to set up this systems of equations. A coin bank contains 27 coins, all nickels, dimes, or quarters. The combined value of the nickels and dimes is $0.90. The combined value of the dimes and quarters is $4. How many coins of each type are in the bank?
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Algebra.Com's Answer #665013 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi!  I'm Edwin McCravy.  AnlytcPhil is my alias! :)\r\n" );
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document.write( "I promised you I'd solve it later.  I notice the other tutor\r\n" );
document.write( "has already solved it correctly in the meantime, but not \r\n" );
document.write( "with a matrix.\r\n" );
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\n" ); document.write( "A coin bank contains 27 coins, all nickels, dimes, or quarters.
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document.write( "N + D + Q = 27\r\n" );
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document.write( "0.05N + 0.10D = 0.90\r\n" );
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\n" ); document.write( "The combined value of the dimes and quarters is $4.
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document.write( "0.10D + 0.25Q = 4.00\r\n" );
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document.write( "The system of equations is:\r\n" );
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document.write( "    N +     D +     Q = 27\r\n" );
document.write( "0.05N + 0.10D         = 0.90\r\n" );
document.write( "        0.10D + 0.25Q = 4.00\r\n" );
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document.write( "The matrix is\r\n" );
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document.write( "Multiply the 2nd and 3rd rows each by 100 to clear\r\n" );
document.write( "the decimals:\r\n" );
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document.write( "That's these row operations:\r\n" );
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document.write( "100R2->R2\r\n" );
document.write( "100R3->R3\r\n" );
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document.write( "Divide the 2nd and 3rd rows each by 5:\r\n" );
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document.write( "R2/5->R2\r\n" );
document.write( "R3/5->R3\r\n" );
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document.write( "To get a 0 where the 1 is on the 2nd row,\r\n" );
document.write( "multiply the 1st row by -1 and add to the 2nd row:\r\n" );
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document.write( "-1R1+R2->R2\r\n" );
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document.write( "To get a 0 where the 2 is on the bottom row,\r\n" );
document.write( "multiply the 2nd row by -2 and add to the bottom\r\n" );
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document.write( "That's -2R2+R3->R3\r\n" );
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document.write( "Divide the bottom row through by 7 to\r\n" );
document.write( "get a 1 where the 7 is:\r\n" );
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document.write( "R3/y->R3\r\n" );
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document.write( "That's the system:\r\n" );
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document.write( "x + y + z = 27\r\n" );
document.write( "    y - z = -9\r\n" );
document.write( "        z = 14\r\n" );
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document.write( "Substitute 14 for z in the 2nd equation:\r\n" );
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document.write( "    y - z = -9\r\n" );
document.write( "   y - 14 = -9\r\n" );
document.write( "        y = 5\r\n" );
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document.write( "Substitute 14 for z and 5 for y in the 1st equation \r\n" );
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document.write( " x + y + z = 27\r\n" );
document.write( "x + 5 + 14 = 27\r\n" );
document.write( "    x + 19 = 27\r\n" );
document.write( "         x = 8\r\n" );
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document.write( "So there are 8 nickels, 5 dimes and 14 quarters.\r\n" );
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document.write( "Edwin
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