document.write( "Question 1021760: Determine how many different sums of money can be made with 2 pennies and 3 nickels. \n" ); document.write( "

Algebra.Com's Answer #805376 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "The first thought that comes to a mind is  (2+1)*(3+1) = 3*4 = 12  possible combinations,\r\n" );
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document.write( "providing  2+1 = 3 choices for pennies (1, 2, 0)  and \r\n" );
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document.write( "           3+1 = 4 choices for nickels (1, 2, 3, 0).\r\n" );
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document.write( "    +---------------------------------------------------+\r\n" );
document.write( "    |  We ONLY should check that, combining this way,   |\r\n" );
document.write( "    |  we get all different values of the total sum.    |\r\n" );
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document.write( "For it, I created the corresponding rectangular table with two inputs. \r\n" );
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document.write( "One input is the most left vertical column for the number of pennies p = (0,1,2),\r\n" );
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document.write( "and the other input is the most upper line for the number of nickels  n = (0,1,2,3).\r\n" );
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document.write( "The cells in the Table are the values of the total sum\r\n" );
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document.write( "      Sum = 1*p + 5*n.\r\n" );
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document.write( "  \r\n" );
document.write( "        T       A       B       L      E\r\n" );
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document.write( "        	0	1	2	3\r\n" );
document.write( "       0	0	5	10	15\r\n" );
document.write( "       1	1	6	11	16\r\n" );
document.write( "       2	2	7	12	17\r\n" );
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document.write( "As you see, the values in the Table are all UNIQUE, so we really have 3*4 = 12 opportunities,\r\n" );
document.write( "if 0 (zero, ZERO) 0 pennies and 0 nickels is allowed;\r\n" );
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document.write( "or 12-1 = 11 possibilities, if this degenerated case is not allowed.\r\n" );
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