document.write( "Question 39847: If you have only 5 cent stamps and 3 cent stamps, how many ways can you put 23 cents postage on a letter?\r
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\n" ); document.write( "\n" ); document.write( "Also There are 145 students in a classs. If each student greeted and shook hands with every other student in the class, how many handshakes would there be?
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Algebra.Com's Answer #25280 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
If you have only 5 cent stamps and 3 cent stamps, how many\r\n" );
document.write( "ways can you put 23 cents postage on a letter?\r\n" );
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document.write( "Let x = the number of 5 cent stamps and y = the \r\n" );
document.write( "number of 3 cent stamps\r\n" );
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document.write( "5x + 3y = 23\r\n" );
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document.write( "6x - x + 3y = 24 - 1\r\n" );
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document.write( "2x - x/3 + y = 8 - 1/3\r\n" );
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document.write( "2x + y - 8 = x/3 - 1/3 = A\r\n" );
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document.write( "Note: The right side above must be an integer because\r\n" );
document.write( " the\r\n" );
document.write( "left side is.  Let this integer be A\r\n" );
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document.write( "x/3 - 1/3 = A\r\n" );
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document.write( "x - 1 = 3A\r\n" );
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document.write( "x = 3A + 1\r\n" );
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document.write( "2x + y - 8 = A\r\n" );
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document.write( "2(3A + 1) + y - 8 = A\r\n" );
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document.write( "6A + 2 + y - 8 = A\r\n" );
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document.write( "y = 6 - 5A\r\n" );
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document.write( "Now since x > 0 and y > 0\r\n" );
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document.write( "3A + 1 > 0 and 6 - 5A > 0\r\n" );
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document.write( "A > -1/3  and A < 6/5\r\n" );
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document.write( "-1/3 < A < 6/5\r\n" );
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document.write( "Two integers are possible for A, 0 and 1\r\n" );
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document.write( "For A = 0 and x = 3A + 1 = 3(0) + 1 = 1\r\n" );
document.write( "             y = 6 - 5A = 6 - 5(0) = 6 \r\n" );
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document.write( "So one solution is 1 5-cent stamp and 6 3-cent\r\n" );
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document.write( "For A = 1 and x = 3A + 1 = 3(1) + 1 = 4\r\n" );
document.write( "             y = 6 - 5A = 6 - 5(1) = 1\r\n" );
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document.write( "So the other solution is 4 5-cent stamps and \r\n" );
document.write( "1 3-cent stamp.\r\n" );
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document.write( "Edwin
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