document.write( "Question 1012290: Jen, Kathy, and Lou work Together. The ratio of Jen's salary to Kathy's salary is 4:3. Lou makes $4,000 more than Kathy does. If the total of their salaries is $134,000, how much does each person make? \n" ); document.write( "

Algebra.Com's Answer #628170 by ikleyn(52799) $\"\"$ $\"About$

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\n" ); document.write( "Jen, Kathy, and Lou work Together. The ratio of Jen's salary to Kathy's salary is 4:3. Lou makes $4,000 more than Kathy does.
\n" ); document.write( "If the total of their salaries is $134,000, how much does each person make?
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document.write( "Mathematical model is this system of equations\r\n" );
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document.write( " = ,                  (1)\r\n" );
document.write( "K + 4000 = L,             (2)\r\n" );
document.write( "J + K + L = 134000,       (3)\r\n" );
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document.write( "or\r\n" );
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document.write( "J = ,               (4)\r\n" );
document.write( "K = L - 4000,             (5)\r\n" );
document.write( "J + K + L = 134000.       (6)\r\n" );
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document.write( "Express J via L by substituting (5) into (4): \r\n" );
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document.write( "J = .       (7)\r\n" );
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document.write( "Now substitute (7) and (5) into (6). You will get a single equation for L:\r\n" );
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document.write( " = 134000.\r\n" );
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document.write( "Multiply both sides by 3:\r\n" );
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document.write( "4*(L-4000) + 3*(L-4000) + 3L = 134000*3 = 402000.\r\n" );
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document.write( "Simplify and solve for L:\r\n" );
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document.write( "10L - 28000 = 402000  ----->   10L = 430000  -----> L =  = 43000.\r\n" );
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document.write( "Now you can easily find the rest of unknowns: \r\n" );
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document.write( "K = L - 4000 = 43000 - 4000 = 39000,\r\n" );
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document.write( "J =  =  = 4*13000 = 52000.\r\n" );
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document.write( "Answer. J = 52000, K = 39000, L = 43000.\r\n" );
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