document.write( "Question 83821: The demand equation for a certain type of printer is given by D=-200p+35,500. The supply equation is predicted to be S=-p^2+400p-20,000. Find the equilibrium price. \n" ); document.write( "
Algebra.Com's Answer #60433 by ankor@dixie-net.com(22740)\"\" \"About 
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The demand equation for a certain type of printer is given by D=-200p+35,500. The supply equation is predicted to be S=-p^2+400p-20,000. Find the equilibrium price.
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\n" ); document.write( "This occurs when Demand (D) = Supply (S) so put the two equations equal to each other:
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\n" ); document.write( "-200p + 35500 = -p^2 + 400p - 20000
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\n" ); document.write( "p^2 - 200p - 400p + 35500 + 20000 = 0; Arrange all terms on the left
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\n" ); document.write( "p^2 - 600p + 55500 = 0; our old friend the quadratic equation
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\n" ); document.write( "Use the quadratic formula to find p: a=1; b=-600; c=55500
\n" ); document.write( "\"p+=+%28-%28-600%29+%2B-+sqrt%28-600%5E2+-+4+%2A+1+%2A+55500+%29%29%2F%282%2A1%29+\"
\n" ); document.write( "\"p+=+%28%2B600+%2B-+sqrt%28360000+-+222000+%29%29%2F%282%29+\"
\n" ); document.write( "\"p+=+%28%2B600+%2B-+sqrt%28138000+%29%29%2F%282%29+\"
\n" ); document.write( "\"p+=+%28600+%2B-+371.5%29%2F2\"
\n" ); document.write( "Two solutions:
\n" ); document.write( "\"p+=+971.5%2F2\"
\n" ); document.write( "p = $485.75
\n" ); document.write( "and
\n" ); document.write( "\"p+=+228.5%2F2\"
\n" ); document.write( "p = $114.25
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\n" ); document.write( "Check solution using the $485.75 price, using a calc see if they are equal:
\n" ); document.write( "-200p + 35500 =
\n" ); document.write( "-200(485.75) + 35500 = -61650
\n" ); document.write( ":
\n" ); document.write( "-p^2 + 400p - 20000
\n" ); document.write( "-(485.75^2) + 400(485.75) - 20000 = -61653;
\n" ); document.write( "Since this produces a negative value, it's probably the lower price we want
\n" ); document.write( ":
\n" ); document.write( "Check the p= $114.25 solution the same way.
\n" ); document.write( "-200(114.25) + 35500 = 12650
\n" ); document.write( "-(114.25^2) + 400(114.25) - 20000 = 12647; close enough \n" ); document.write( "
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