document.write( "Question 257726: How many ways can you make $0.25 using pennies, nickels, dimes, and quarters
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Algebra.Com's Answer #189608 by Edwin McCravy(20056)\"\" \"About 
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document.write( "p + 5n + 10d + 25q = 25\r\n" );
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document.write( "There is just one way to have 25 cents with only 1 quarter.\r\n" );
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document.write( "1.  1 quarter = $0.25\r\n" );
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document.write( "So for all the other ways we only have pennies, nickels and dimes.\r\n" );
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document.write( "p + 5n + 10d = 25\r\n" );
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document.write( "The number of pennies must be a multiple of 5 (including 0)\r\n" );
document.write( "So let p = 5k where k is an integer \r\n" );
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document.write( "5k + 5n + 10d = 25\r\n" );
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document.write( "Divide through by 5\r\n" );
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document.write( "k + n + 2d = 5\r\n" );
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document.write( "     k + n = 5 - 2d\r\n" );
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document.write( "So d can only be 0 thru 2 and have the right side positive.\r\n" );
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document.write( "For d = 0, we have\r\n" );
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document.write( "k + n = 5, there are 6 possibilities, k = 0 thru 5 and n = 5 thru 0 \r\n" );
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document.write( "2.  k=0, 0 pennies, 5 nickels, 0 dimes = $0.25\r\n" );
document.write( "3.  k=1, 5 pennies, 4 nickels, 0 dimes = $0.25\r\n" );
document.write( "4.  k=2, 10 pennies, 3 nickels, 0 dimes = $0.25\r\n" );
document.write( "5.  k=3, 15 pennies, 2 nickels, 0 dimes = $0.25\r\n" );
document.write( "6.  k=4, 20 pennies, 1 nickels, 0 dimes = $0.25\r\n" );
document.write( "7.  k=5, 25 pennies, 0 nickels, 0 dimes = $0.25\r\n" );
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document.write( "For d = 1, we have\r\n" );
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document.write( "k + n = 3, there are 4 possibilities, k = 0 thru 3 and n = 3 thru 0 \r\n" );
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document.write( "8.  k=0, 0 pennies, 3 nickels, 1 dime = $0.25\r\n" );
document.write( "9.  k=1, 5 pennies, 2 nickels, 1 dime = $0.25\r\n" );
document.write( "10.  k=2, 10 pennies, 1 nickels, 1 dime = $0.25\r\n" );
document.write( "11.  k=3, 15 pennies, 0 nickels, 1 dime = $0.25\r\n" );
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document.write( "For d = 2, we have\r\n" );
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document.write( "k + n = 1, there are 2 possibilities, k = 0 thru 1 and n = 1 thru 0\r\n" );
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document.write( "12.  k=0, 0 pennies, 1 nickel, 2 dimes = $0.25\r\n" );
document.write( "13.  k=1, 5 pennies, 0 nickels, 2 dimes = $0.25\r\n" );
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document.write( "So the total is 1 + 6 + 4 + 2 = 13 ways.\r\n" );
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document.write( "Edwin
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