document.write( "Question 1119320: A boy has 180 coins altogether . There are nickels dimes and quarters. Number of dimes is half the number of nickels and quarters. Value of coins is 16. How many of each kind of coin does he have
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Algebra.Com's Answer #734809 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "A boy has 180 coins altogether. There are nickels dimes and quarters. Number of dimes is half the number of nickels and quarters.
\n" ); document.write( "Value of coins is 16 $\"highlight%28dollars%29\"$ . How many of each kind of coin does he have
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document.write( "Let x be the number of dimes.\r\n" );
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document.write( "Then the number of nickels and dimes (altogether) is 2x, according to the condition.\r\n" );
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document.write( "The total number of coins is 180 = x + 2x = 3x,  which implies that the number of dimes is  x =  = 60.\r\n" );
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document.write( "Thus you conclude that total number of nickels and quarters is 180 - 60 = 120, and their value is  16-60*0.1 = 10 dollars.\r\n" );
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document.write( "Now, let Q be the unknown number of quarters.\r\n" );
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document.write( "Then the number of nickels is (120-Q), and the value equation for nickels and quarters is\r\n" );
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document.write( "    5*(120-Q) + 25Q = 1000    (cents,  or $10).\r\n" );
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document.write( "Simplify and solve for Q:\r\n" );
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document.write( "    600 - 5Q + 25Q = 1000,\r\n" );
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document.write( "    20Q = 1000 - 600 = 400  ====>  Q =  = 20.\r\n" );
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document.write( "Answer.  20 quarters, (120-20) = 100 nickels and 60 dimes.\r\n" );
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