document.write( "Question 1191337: Hi
\n" ); document.write( "If Bob had twice as many nickels and half as many quarters, he would have 60c less. Suppose he now has 16 nickels and quarters. How many of each coin does he have.
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Algebra.Com's Answer #823162 by ikleyn(53763) $\"\"$ $\"About$

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\n" ); document.write( "If Bob had twice as many nickels and half as many quarters, he would have 60c less.
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document.write( "N = # of nickels\r\n" );
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document.write( "Q = # of quarters\r\n" );
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document.write( "Equations from the condition\r\n" );
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document.write( "    N + Q = 16                           (1)\r\n" );
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document.write( "    5*(2N) +  = 5N + 25Q - 60    (2)\r\n" );
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document.write( "Simplify (2) by multiplying both sides of the equation by 2\r\n" );
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document.write( "    20N + 25Q = 10N + 50Q - 120\r\n" );
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document.write( "    10N - 25Q = -120\r\n" );
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document.write( "     2N -  5Q =  -24                    (3)\r\n" );
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document.write( "Thus we have the system of two equations, (1) and (3)\r\n" );
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document.write( "     N +  Q =  16      (1')\r\n" );
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document.write( "    2N - 5Q = -24      (3')\r\n" );
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document.write( "Solve by substitution. For it, express  Q = 16-N from (1') and substitute it into (3').\r\n" );
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document.write( "    2N - 5*(16-N) = -24 \r\n" );
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document.write( "    2N - 80 + 5N  = -24\r\n" );
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document.write( "      4N + 5N     = -24 + 80\r\n" );
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document.write( "         7N       =  56\r\n" );
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document.write( "          N       = 56/7 = 8.\r\n" );
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document.write( "ANSWER.  8 nickels and 16-8 = 8 quarters.\r\n" );
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