document.write( "Question 1078159: Use a generating function to model the problem: How many ways are there to make change for $0.62 using only pennies, nickels, and dimes so that the total number of coins used is even? \n" ); document.write( "

Algebra.Com's Answer #692629 by ikleyn(52905) $\"\"$ $\"About$

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document.write( "1.  On the method of generating function/functions to solve coin problems see the pretty fine explanation at the link\r\n" );
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document.write( "    http://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15251-f10/Site/Materials/Lectures/Lecture09/lecture09.pdf\r\n" );
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document.write( "    http://www.cs.cmu.edu/afs/cs.cmu.edu/academic/class/15251-f10/Site/Materials/Lectures/Lecture09/lecture09.pdf\r\n" );
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document.write( "2.  But I think that the GIVEN particular problem can be solved faster and easier DIRECTLY and EXPLICITLY:\r\n" );
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document.write( "   2 pennies  +  0 dimes   + 12 nickels\r\n" );
document.write( "   2 pennies  +  2 dimes   +  8 nickels\r\n" );
document.write( "   2 pennies  +  4 dimes   +  4 nickels\r\n" );
document.write( "   2 pennies  +  6 dimes   +  0 nickels\r\n" );
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document.write( "   7 pennies  +  0 dimes   + 11 nickels\r\n" );
document.write( "   7 pennies  +  2 dimes   +  7 nickels\r\n" );
document.write( "   7 pennies  +  4 dimes   +  3 nickels\r\n" );
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document.write( "  12 pennies  +  0 dimes   + 10 nickels\r\n" );
document.write( "  12 pennies  +  2 dimes   +  6 nickels\r\n" );
document.write( "  12 pennies  +  4 dimes   +  2 nickels\r\n" );
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document.write( "  17 pennies  +  0 dimes   +  9 nickels\r\n" );
document.write( "  17 pennies  +  2 dimes   +  5 nickels\r\n" );
document.write( "  17 pennies  +  4 dimes   +  1 nickels\r\n" );
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document.write( "  22 pennies  +  0 dimes   +  8 nickels\r\n" );
document.write( "  22 pennies  +  2 dimes   +  4 nickels\r\n" );
document.write( "  22 pennies  +  4 dimes   +  0 nickels\r\n" );
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document.write( "  27 pennies  +  0 dimes   +  7 nickels\r\n" );
document.write( "  27 pennies  +  2 dimes   +  3 nickels\r\n" );
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document.write( "  32 pennies  +  0 dimes   +  6 nickels\r\n" );
document.write( "  32 pennies  +  2 dimes   +  2 nickels\r\n" );
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document.write( "  37 pennies  +  0 dimes   +  5 nickels\r\n" );
document.write( "  37 pennies  +  2 dimes   +  1 nickels\r\n" );
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document.write( "  42 pennies  +  0 dimes   +  4 nickels\r\n" );
document.write( "  42 pennies  +  2 dimes   +  0 nickels\r\n" );
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document.write( "  47 pennies  +  0 dimes   +  3 nickels\r\n" );
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document.write( "  52 pennies  +  0 dimes   +  2 nickels\r\n" );
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document.write( "  57 pennies  +  0 dimes   +  1 nickels\r\n" );
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document.write( "  62 pennies  +  0 dimes   +  0 nickels\r\n" );
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document.write( "In this way I counted 28 possibilities.\r\n" );
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document.write( "So, my answer is:  28 possibilities.\r\n" );
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