document.write( "Question 1154160: An 150-unit apartment complex currently collects $90,000 per month in rent. Rent on each apartment is $600. The new management company wants to increase revenues to $113,400. But for each $25 increase, two tenants will move out. How many rent increases will be needed to produce revenue of $113,400? \n" ); document.write( "

Algebra.Com's Answer #776527 by ikleyn(52777) $\"\"$ $\"About$

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document.write( "From the condition, when the rent price is  600 + 25i, where i is the number of the 25-dollar increments,\r\n" );
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document.write( "the number of units occupied is \r\n" );
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document.write( "    N(i) = 150 - 2i.\r\n" );
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document.write( "So, the revenue is  R(i) = (600+25i)*N(i) = (600+25i)*(150-2i).\r\n" );
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document.write( "We want to find \" i \" in a way to get  R(i) = 113400.\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "    (600+25i)*(150-2i) = 113400.\r\n" );
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document.write( "Simplify and solve for \" i \"\r\n" );
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document.write( "     90000 + 3750i - 1200i - 50i^2 = 113400\r\n" );
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document.write( "     50i^2 - 2550i + 23400 = 0\r\n" );
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document.write( "       i^2 - 51i + 468 = 0\r\n" );
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document.write( "      =  = .\r\n" );
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document.write( "Case 1.  i =  =  12.\r\n" );
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document.write( "         It means 12 increments by 25 dollars each; so, the new price is 600+12*25 = 900 dollars.\r\n" );
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document.write( "     \r\n" );
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document.write( "Case 2.  i =  =  39.\r\n" );
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document.write( "         It means 39 increments by 25 dollars each; so, the new price is 600+39*25 = 1575 dollars.\r\n" );
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document.write( "ANSWER.  There are two answers,  900 dollars and  1575 dollars.\r\n" );
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