document.write( "Question 1111565: Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2225. What was the rate charged per hour by each mechanic if the sum of the two rates was 130 per hour? \n" ); document.write( "

Algebra.Com's Answer #726565 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x be the hourly rate of the first mechanic in dollars per hour, and\r\n" );
document.write( "let y be the hourly rate of the second mechanic. \r\n" );
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document.write( "Then from the condition, you have this system of two linear equations\r\n" );
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document.write( "20x + 15y = 2225,    (1)  \r\n" );
document.write( "  x +   y =  130.    (2)\r\n" );
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document.write( "From equation (2), express y = 130 - x and substitute it into equation (1), replacing y. \r\n" );
document.write( "You will get a single equation for only one unknown\r\n" );
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document.write( "20x + 15*(130-x) = 2225  dollars.     (3)\r\n" );
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document.write( "Simplify and solve for x:\r\n" );
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document.write( "20x + 1950 - 15x = 2225  ====>\r\n" );
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document.write( "5x = 2225 - 1950 = 275  ====>  x =  = 55.\r\n" );
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document.write( "Thus the first mechanic's rate is $55 per hour.\r\n" );
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document.write( "Then the second mechanic's rate is $130 - $55 = $75 per hour.\r\n" );
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document.write( "Let x be the rate of the first mechanic in dollars per hour.\r\n" );
document.write( "Then the rate of the second mechanic is (130-x) dollars per hour.\r\n" );
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document.write( "The \"amount\" equation is\r\n" );
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document.write( "20x + 15*(130-x) = 2225  dollars.\r\n" );
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document.write( "It is the same equation (3) of the PREVIOUS solution, and it leads to the same answer.\r\n" );
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\n" ); document.write( "For similar solved problems see the lesson\r
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