document.write( "Question 341148: What are the different combinations of nickels, dimes, and/or quarters that equal exactly 45 cents? \n" ); document.write( "

Algebra.Com's Answer #244310 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "5n + 10d + 25q = 45\r\n" );
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document.write( "It can be divided through by 5\r\n" );
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document.write( "n + 2d + 5q = 9\r\n" );
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document.write( "We will consider two cases\r\n" );
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document.write( "Case 1.  Using no quarters, i.e., q=0, then\r\n" );
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document.write( "n + 2d + 5(0) = 9\r\n" );
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document.write( "n + 2d = 9\r\n" );
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document.write( "d = \r\n" );
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document.write( "n must be an odd number to make the numerator even so it\r\n" );
document.write( "can be divided evenly by the denominator 2.\r\n" );
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document.write( "1.  n=1 nickel, 4 dimes\r\n" );
document.write( "2.  n=3 nickels, 3 dimes.\r\n" );
document.write( "3.  n=5 nickels, 2 dimes.\r\n" );
document.write( "4.  n=7 nickels, 1 dime.\r\n" );
document.write( "5.  n=9 nickels, 0 dimes.\r\n" );
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document.write( "Case 2. q=1\r\n" );
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document.write( "n + 2d + 5(1) = 9\r\n" );
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document.write( "n + 2d + 5 = 9\r\n" );
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document.write( "n + 2d = 4\r\n" );
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document.write( "d = \r\n" );
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document.write( "n must be an even number to make the numerator even so it\r\n" );
document.write( "can be divided evenly by the denominator 2.  (Don't forget\r\n" );
document.write( "that 0 is an even number!)\r\n" );
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document.write( "6.  n=0 nickels, 2 dimes\r\n" );
document.write( "7.  n=2 nickels, 1 dime.\r\n" );
document.write( "8.  n=4 nickels, 0 dimes.\r\n" );
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document.write( "So there are 8 ways to make 45 cents using nickels and/or dimes and/or \r\n" );
document.write( "quarters. \r\n" );
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document.write( "Edwin

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