document.write( "Question 1024618: System of Two Linear Equation : if man has $315 in ten and five dollar bills, how many of each does he have if he has 42 bills in all? \n" ); document.write( "

Algebra.Com's Answer #640016 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "System of Two Linear Equation : if man has $315 in ten and five dollar bills, how many of each does he have if he has 42 bills in all?
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document.write( " f +   t =  42,   (1)     (f = # of 5-dollar bills)\r\n" );
document.write( "5f + 10t = 315.   (2)     (t = # of 10-dollar bills)\r\n" );
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document.write( "Express f = 42-t from (1) and substitute it into (2). You will get a single equation for t\r\n" );
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document.write( "5*(42-t) + 10t = 315.\r\n" );
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document.write( "Simplify and solve it:\r\n" );
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document.write( "210 - 5t + 10t = 315,\r\n" );
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document.write( "5t = 315 - 210,\r\n" );
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document.write( "5t = 105,\r\n" );
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document.write( "t =  = 21.\r\n" );
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document.write( "Thus there are 21 of 10-dollar bills.\r\n" );
document.write( "Then the number of 5-dollar bills is 42-21 = 21.\r\n" );
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document.write( "Check: 5*21 + 10*21 = 105 + 210 = 315.   OK.\r\n" );
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