document.write( "Question 1199919: A piggy bank contains only nickels, dimes, and quarters. There is a total of 105 coins and the total value of those coins is $10.75.\r
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\n" ); document.write( "\n" ); document.write( "n=nickel
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Algebra.Com's Answer #834056 by MathTherapy(10555)\"\" \"About 
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document.write( "A piggy bank contains only nickels, dimes, and quarters. There is a total of 105 coins and the total value of those coins is $10.75.\r\n" );
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document.write( "Find a general solution of the number of each coin.\r\n" );
document.write( "Use the general solutions from part 1 to list 3 specific solutions (for n, d, & q).\r\n" );
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document.write( "n=nickel\r\n" );
document.write( "d=dime\r\n" );
document.write( "q=a quarter\r\n" );
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document.write( "Since number of nickels, dimes, and quarters are n, d, and q, we get the following COIN-COUNT equation:\r\n" );
document.write( "  n + d + q = 105 --- eq (i), and total value-equation, .05n + .1d + .25q = 10.75, or 20(.05n + .1d + .25q) = 20(10.75), or\r\n" );
document.write( "n + 2d + 5q = 215 --- eq (ii)\r\n" );
document.write( "     d + 4q = 110 ----- Subtracting eq (i) from eq (ii) \r\n" );
document.write( "         4q = 110 - d \r\n" );
document.write( "         \"matrix%281%2C3%2C+q%2C+%22=%22%2C+%28110+-+d%29%2F4%29\" ----- Solving for q ----- eq (iii)\r\n" );
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document.write( "The SMALLEST number of dimes (d) that can be substituted         The next \"d\" integer-value that'll create the next      \r\n" );
document.write( "into the above equation, and which also yields an                smaller integer in numerator that's a MULTIPLE of 4 is 6,\r\n" );
document.write( "INTEGER-number of quarters is 2, since 2 leads to a              since 6 leads to a numerator of 104, a multiple of 4, and                       \r\n" );
document.write( "numerator of 108, a MULTIPLE of 4 (the denominator).             which also yields an INTEGER-VALUE for q.\r\n" );
document.write( "      We then get:                                            We then get: \r\n" );
document.write( "Therefore, for the above, we get: Number of dimes: 2               Therefore, for the above, we get: Number of dimes: 6                              \r\n" );
document.write( "Number of quarters: 27                                             Number of quarters: 26\r\n" );
document.write( "Number of nickels, 105 - (2 + 27) = 105 - 29 = 76                  Number of nickels, 105 - (6 + 26) = 105 - 32 = 73\r\n" );
document.write( "This gives us, (n, d, q) = (76, 2, 27)                             This gives us, (n, d, q) = (73, 6, 26)\r\n" );
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document.write( "                                          So far, we have: (n, d, q) = (76, 2, 27)\r\n" );
document.write( "                                                           (n, d, q) = (73, 6, 26)\r\n" );
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document.write( "Looking at the above SEQUENCE, it's quite obvious that the nickels decrease by 3, the\r\n" );
document.write( "                                                           dimes INCREASE by 4, and the\r\n" );
document.write( "                                                           quarters DECREASE by 1. \r\n" );
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document.write( "                               Thus, we get the following: (n, d, q) = (76,  2, 27)\r\n" );
document.write( "                                                           (n, d, q) = (73,  6, 26)\r\n" );
document.write( "                                                           (n, d, q) = (70, 10, 25)\r\n" );
document.write( "                                                           (n, d, q) = (67, 14, 24)\r\n" );
document.write( "                                                           (n, d, q) = (64, 18, 23)\r\n" );
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document.write( "You don't need that many because you were asked for just 3, but you should get the \"picture.\" CAPISCHE?
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