document.write( "Question 1142571: A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 8%, and the tax in the second city was 4%. The total hotel tax paid for the two cities was $640. How much was the hotel charge in each city before tax? \n" ); document.write( "

Algebra.Com's Answer #763249 by ikleyn(52832) $\"\"$ $\"About$

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document.write( "Let x = the hotel charge before tax in the first city;\r\n" );
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document.write( "    y = that of the second city.\r\n" );
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document.write( "Then from the condition you have these two equations in two unknowns\r\n" );
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document.write( "       x  -     y = 500     (1)\r\n" );
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document.write( "    0.08x + 0.04y = 640.    (2)\r\n" );
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document.write( "To solve the system of equations, use the Elimination method.\r\n" );
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document.write( "For it, from equation (1) express  x = 500 + y  and substitute it into the second equation. You will get\r\n" );
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document.write( "    0.08*(500+y) + 0.04y = 640.\r\n" );
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document.write( "Simplify and solve for y\r\n" );
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document.write( "    40 + 0.08y + 0.04y = 640\r\n" );
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document.write( "    0.12y = 640 - 40 = 600\r\n" );
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document.write( "    y = 600/0.12 = 5000.\r\n" );
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document.write( "ANSWER.  In the second city hotel charged $5000;  in the second city  $500 dollars more, or  5500  dollars.\r\n" );
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document.write( "CHECK.   0.08*5500 + 0.04*5000 = 640  dollars.    ! Correct !\r\n" );
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