document.write( "Question 1152967: A furniture shop refinishes tables. Employees use one of two methods to refinish each table. Method I takes 0.5hours and the material costs$9.Method II takes2 hours, and the material costs$7.Next week, they plan to spend 99 hours in labor and $564 in material for refinishing tables. How many tables should they plan to refinish with each method? \n" ); document.write( "

Algebra.Com's Answer #775107 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "Let x be the number of Tables by the Method 1, and\r\n" );
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document.write( "let y be the number of Tables by the Method 2.\r\n" );
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document.write( "Then you have this system of 2 equations in 2 unknowns\r\n" );
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document.write( "    0.5x + 2y = 99        (1)    (hours)    \r\n" );
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document.write( "    9x   + 7y = 564.      (2)    (labor cost)\r\n" );
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document.write( "To solve it,  Multiply equation (1) by 18 (both sides).  Keep equation (2) as is.\r\n" );
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document.write( "    9x +  36y = 99*18     (3)   \r\n" );
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document.write( "    9x   + 7y = 564.      (4)   \r\n" );
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document.write( "Subtract equation (4) from equation (3). You will get\r\n" );
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document.write( "    36y - 7y = 99*18 - 564\r\n" );
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document.write( "    29y      = 1218\r\n" );
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document.write( "      y      = 1218/29 = 42.\r\n" );
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document.write( "Substitute the found value of y into equation (1) and find x\r\n" );
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document.write( "     0.5x + 2*42 = 99,\r\n" );
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document.write( "     0.5x = 99 - 2*42 = 15\r\n" );
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document.write( "        x             = 15/0.5 = 30.\r\n" );
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document.write( "ANSWER.  30 tables by Method 1  and  42 tables by Method 2.\r\n" );
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