document.write( "Question 1198674: A furniture shop refinishes chairs. Employees use 2 methods to refinish the chairs. Method 1 takes 0.5 hours and the material cost 10$. Method 2 takes 2.0 hours, and the material costs 7$. Next week, they plan to spend 98 hours in labor and 508$ in material for refinishing chairs. How many chairs should they plan to refinish with each method?(round to two decimal places if necessary) \n" ); document.write( "

Algebra.Com's Answer #832305 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "A furniture shop refinishes chairs. Employees use 2 methods to refinish the chairs.
\n" ); document.write( "Method 1 takes 0.5 hours and the material cost 10$.
\n" ); document.write( "Method 2 takes 2.0 hours, and the material costs 7$.
\n" ); document.write( "Next week, they plan to spend 98 hours in labor and 508$ in material for refinishing chairs.
\n" ); document.write( "How many chairs should they plan to refinish with each method?
\n" ); document.write( "(round to two decimal places if necessary)
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\n" ); document.write( "\n" ); document.write( " The rounding instruction is absurdist, since the answer must be in integer numbers.\r
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document.write( "Let x be the number of chairs by Method 1;\r\n" );
document.write( "    y be the number of chairs by Method 2.\r\n" );
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document.write( "Write equations as you read the problem\r\n" );
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document.write( "    0.5x + 2y = 98    (hours of labor)    (1)\r\n" );
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document.write( "     10x + 7y = 508    (dollars)          (2)\r\n" );
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document.write( "To solve, multiply equation (1) by 20; then subtract equation (2) from it.\r\n" );
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document.write( "You will get simple equation for single unknown y\r\n" );
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document.write( "           20*2y - 7y = 20*98 - 508\r\n" );
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document.write( "or\r\n" );
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document.write( "                33y   =    1452\r\n" );
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document.write( "                  y   =    1452/33 = 44.\r\n" );
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document.write( "Having y= 44, find x from equation (2)\r\n" );
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document.write( "    10x + 7*44 = 508\r\n" );
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document.write( "    10x = 508 - 7*44 = 200\r\n" );
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document.write( "      x              = 200/10 = 20.\r\n" );
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document.write( "ANSWER.  10 chairs by Method 1 and 44 chairs by Method 2.\r\n" );
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