document.write( "Question 486666: In how many different ways can you make change for one dollar without using pennies? \n" ); document.write( "
Algebra.Com's Answer #332671 by Edwin McCravy(20060)\"\" \"About 
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document.write( "There are three major cases,\r\n" );
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document.write( "Major case I.  Using no half dollars\r\n" );
document.write( "Major case II.  Using exactly 1 half dollar.\r\n" );
document.write( "Major case III.  Using two half dolars.\r\n" );
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document.write( "I.  Using 0 half dollars.\r\n" );
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document.write( "There are 4 sub-cases. \r\n" );
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document.write( "Sub-Case A.  Using 0 quarters,\r\n" );
document.write( "Sub-Case B.  Using exactly 1 quarter\r\n" );
document.write( "Sub-Case C.  Using exactly 2 quarters\r\n" );
document.write( "Sub-Case D.  Using exactly 3 quarters\r\n" );
document.write( "Sub-Case E.  Using exactly 4 quarters.\r\n" );
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document.write( "Sub-Case A:\r\n" );
document.write( "If you don't use any quarters you can use from 0 up to 10 dimes, and the\r\n" );
document.write( "rest, if any, can be had all in nickels.  That's 11 possible ways to use \r\n" );
document.write( "no quarters.\r\n" );
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document.write( "Sub-Case B:\r\n" );
document.write( "If you use exactly 1 quarter you can use from 0 up to 7 dimes, and the\r\n" );
document.write( "rest can be had all in nickels.  That's 8 possible ways to use \r\n" );
document.write( "1 quarters.\r\n" );
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document.write( "Sub-Case C:\r\n" );
document.write( "If you use exactly 2 quarters you can use from 0 up to 5 dimes, and the\r\n" );
document.write( "rest, if any, can be had all in nickels.  That's 6 possible ways to use \r\n" );
document.write( "2 quarters.\r\n" );
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document.write( "Sub-Case D:\r\n" );
document.write( "If you use exactly 3 quarters you can use from 0 up to 2 dimes, and the\r\n" );
document.write( "rest can be had all in nickels.  That's 3 possible ways to use \r\n" );
document.write( "3 quarters.\r\n" );
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document.write( "Sub-Case E:\r\n" );
document.write( "If you use 4 quarters, that's the whole dollar, so that's 1 more way.\r\n" );
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document.write( "Total from all those sub-cases for Major Case I:\r\n" );
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document.write( "11+8+6+3+1 = 29 ways\r\n" );
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document.write( "----\r\n" );
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document.write( "Major case II.  Using exactly 1  half dollars.  That leaves 50 cents.\r\n" );
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document.write( "There are 3 sub-cases. \r\n" );
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document.write( "Sub-Case A.  Using 0 quarters,\r\n" );
document.write( "Sub-Case B.  Using exactly 1 quarter\r\n" );
document.write( "Sub-Case C.  Using exactly 2 quarters\r\n" );
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document.write( "Sub-Case A:\r\n" );
document.write( "If you don't use any quarters you can use from 0 up to 5 dimes, and the\r\n" );
document.write( "rest, if any, can be had all in nickels.  That's 6 possible ways to use \r\n" );
document.write( "no quarters.\r\n" );
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document.write( "Sub-Case B:\r\n" );
document.write( "If you use exactly 1 quarter you can use from 0 up to 2 dimes, and the\r\n" );
document.write( "rest can be had all in nickels.  That's 3 possible ways to use \r\n" );
document.write( "1 quarters.\r\n" );
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document.write( "Sub-Case C:\r\n" );
document.write( "If you use exactly 2 quarters you have the whole dollar, so that's \r\n" );
document.write( "1 more way.\r\n" );
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document.write( "Total from all those sub-cases for Major Case II:\r\n" );
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document.write( "6+3+1 = 10 ways\r\n" );
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document.write( "----\r\n" );
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document.write( "Major case III.  Using 2 half dollars.\r\n" );
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document.write( "That's the whole dollar.  So that's one more case.\r\n" );
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document.write( "So from major case I, II, and III, we have  29+10+1 = 40 ways.\r\n" );
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document.write( "Answer: 40 ways to change a dollar using only half dollars, quarters,\r\n" );
document.write( "dimes and nickels, no pennies.  If you count changing a paper dollar for\r\n" );
document.write( "a dollar coin, then there are 41 ways.\r\n" );
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document.write( "So the answer is 40 if you don't count 1 silver dollar as a way to change\r\n" );
document.write( "a dollar, and 41 if you do.\r\n" );
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document.write( "Edwin
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