document.write( "Question 103995: Could someone please help me with this tricky word problem???
\n" ); document.write( "The demand and supply equations for a certain item are given by
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Algebra.Com's Answer #75664 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
To find the equilibrium price, set the two equations equal to one another\r
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\n" ); document.write( "\n" ); document.write( "\"-5p%2B40=-p%5E2%2B30p-8\"\r
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\n" ); document.write( "\n" ); document.write( "\"40=-p%5E2%2B30p-8%2B5p\" Add 5p to both sides\r
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\n" ); document.write( "\n" ); document.write( "\"0=-p%5E2%2B30p-8%2B5p-40\" Subtract 40 from both sides\r
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\n" ); document.write( "\n" ); document.write( "\"0=-p%5E2%2B35p-48\" Combine like terms\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for p:\r
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\n" ); document.write( "\n" ); document.write( "Starting with the general quadratic\r
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\n" ); document.write( "\n" ); document.write( "\"ap%5E2%2Bbp%2Bc=0\"\r
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\n" ); document.write( "\n" ); document.write( "the general solution using the quadratic equation is:\r
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\n" ); document.write( "\n" ); document.write( "\"p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"\r
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\n" ); document.write( "\n" ); document.write( "So lets solve \"-p%5E2%2B35%2Ap-48=0\" ( notice \"a=-1\", \"b=35\", and \"c=-48\")\r
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\n" ); document.write( "\n" ); document.write( "\"p+=+%28-35+%2B-+sqrt%28+%2835%29%5E2-4%2A-1%2A-48+%29%29%2F%282%2A-1%29\" Plug in a=-1, b=35, and c=-48\r
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\n" ); document.write( "\n" ); document.write( "\"p+=+%28-35+%2B-+sqrt%28+1225-4%2A-1%2A-48+%29%29%2F%282%2A-1%29\" Square 35 to get 1225 \r
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\n" ); document.write( "\n" ); document.write( "\"p+=+%28-35+%2B-+sqrt%28+1225%2B-192+%29%29%2F%282%2A-1%29\" Multiply \"-4%2A-48%2A-1\" to get \"-192\"\r
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\n" ); document.write( "\n" ); document.write( "\"p+=+%28-35+%2B-+sqrt%28+1033+%29%29%2F%282%2A-1%29\" Combine like terms in the radicand (everything under the square root)\r
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\n" ); document.write( "\n" ); document.write( "\"p+=+%28-35+%2B-+sqrt%281033%29%29%2F%282%2A-1%29\" Simplify the square root (note: If you need help with simplifying the square root, check out this solver)\r
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\n" ); document.write( "\n" ); document.write( "\"p+=+%28-35+%2B-+sqrt%281033%29%29%2F-2\" Multiply 2 and -1 to get -2\r
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\n" ); document.write( "\n" ); document.write( "So now the expression breaks down into two parts\r
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\n" ); document.write( "\n" ); document.write( "\"p+=+%28-35+%2B+sqrt%281033%29%29%2F-2\" or \"p+=+%28-35+-+sqrt%281033%29%29%2F-2\"\r
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\n" ); document.write( "\n" ); document.write( "Now break up the fraction\r
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\n" ); document.write( "\n" ); document.write( "\"p=-35%2F-2%2Bsqrt%281033%29%2F-2\" or \"p=-35%2F-2-sqrt%281033%29%2F-2\"\r
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\n" ); document.write( "\n" ); document.write( "Simplify\r
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\n" ); document.write( "\n" ); document.write( "\"p=35+%2F+2-sqrt%281033%29%2F2\" or \"p=35+%2F+2%2Bsqrt%281033%29%2F2\"\r
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\n" ); document.write( "\n" ); document.write( "So these expressions approximate to\r
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\n" ); document.write( "\n" ); document.write( "\"p=1.4298413200118\" or \"p=33.5701586799882\"\r
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\n" ); document.write( "\n" ); document.write( "So our possible solutions are:\r
\n" ); document.write( "\n" ); document.write( "\"p=1.4298413200118\" or \"p=33.5701586799882\"\r
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\n" ); document.write( "\n" ); document.write( "However, plugging in \"p=33.5701586799882\" results in a negative demand. So the only solution is \"p=1.4298413200118\". So the equilibrium price is about $1.43
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