document.write( "Question 1114184: A box contains $6.15 in nickels , dimes, and quarters. There are 36 coins in all, and the sum of the numbers of nickels and dimes
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Algebra.Com's Answer #729197 by ikleyn(52784) $\"\"$ $\"About$

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\n" ); document.write( "A box contains $6.15 in nickels , dimes, and quarters. There are 36 coins in all, and the sum of the numbers of nickels and dimes
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document.write( "(1)  nickels + dimes + quarters = 36      ( <<<---=== given )\r\n" );
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document.write( "     N       + D     + Q        = 36      ( the same )\r\n" );
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document.write( "(2)  N       + D   = Q - 2                ( <<<---=== given )\r\n" );
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document.write( "========>  Q + (Q-2) = 36\r\n" );
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document.write( "          2Q - 2 = 36  ====>  2Q = 36 + 2 = 38  ====>  Q = 19\r\n" );
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document.write( "So, we found number of quarters.  It is 19.\r\n" );
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document.write( "Next, you can reduce the problem from 3 unknowns to only two of them:\r\n" );
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document.write( "    we have 36-19 = 17 nickels and dimes, that are worth  6.15 - 19*0.25 = 1.40 dollars.\r\n" );
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document.write( " N +   D =  17      (coins)    (1)\r\n" );
document.write( "5N + 10D = 140      (cents)    (2)\r\n" );
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document.write( "Simplify\r\n" );
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document.write( " N +   D =  17                 (1')\r\n" );
document.write( " N +  2D =  28                 (2')\r\n" );
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document.write( "Subtract eq(1') from eq(2').\r\n" );
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document.write( "      D = 28-17 = 11.\r\n" );
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document.write( "Answer.  11 dimes,  19 quarters  and  17-11 = 6 nickels.\r\n" );
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document.write( "Check.   5*6 + 11*10 + 19*25 = 615 cents.   ! Correct !\r\n" );
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