document.write( "Question 104060: The demand and supply equations for a certain item are given by
\n" ); document.write( " D = –5p + 40
\n" ); document.write( " S = –p^2 + 30p – 8
\n" ); document.write( "Find the equilibrium price.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #75879 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
he demand and supply equations for a certain item are given by
\n" ); document.write( "D = –5p + 40
\n" ); document.write( "S = –p^2 + 30p – 8
\n" ); document.write( "Find the equilibrium price.
\n" ); document.write( ":
\n" ); document.write( "The equilibrium price (p) occurs when D = S, therefore:
\n" ); document.write( ":
\n" ); document.write( "-5p + 40 = -p^2 + 30p - 8
\n" ); document.write( ":
\n" ); document.write( "Arrange as a quadratic equation on the left:
\n" ); document.write( "+p^2 - 5p - 30p + 40 + 8 = 0
\n" ); document.write( ":
\n" ); document.write( "p^2 - 35p + 48 = 0
\n" ); document.write( ":
\n" ); document.write( "This equation requires the quadratic formula to solve: a = 1; b =-35; c= 48
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"p+=+%28-%28-35%29+%2B-+sqrt%28-35%5E2+-+4+%2A+1+%2A+48+%29%29%2F%282%2A1%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"p+=+%2835+%2B-+sqrt%281225+-+192+%29%29%2F%282%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"p+=+%2835+%2B-+sqrt%281033+%29%29%2F%282%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"p+=+%2835+%2B-+32.14%29%2F%282%29+\"
\n" ); document.write( "Two solutions
\n" ); document.write( "\"p+=+%2835+%2B+32.14%29%2F%282%29+\"
\n" ); document.write( "\"p+=+%2867.14%29%2F%282%29+\"
\n" ); document.write( "p = 33.57
\n" ); document.write( "and
\n" ); document.write( "\"p+=+%2835+-+32.14%29%2F%282%29+\"
\n" ); document.write( "\"p+=+%282.86%29%2F%282%29+\"
\n" ); document.write( "p = $1.43
\n" ); document.write( ":
\n" ); document.write( "Only the lower price make sense, the higher value will give negative values in the original expressions.
\n" ); document.write( ":
\n" ); document.write( "You can check this by substituting 1.43 for p
\n" ); document.write( "-5(1.43) + 40 = -(1.43^2) + 30p - 8
\n" ); document.write( "-7.15 + 40 = -2.0449 + 30(1.43) - 8
\n" ); document.write( " 32.85 = -2.0449 + 42.9 - 8
\n" ); document.write( " 32.85 = 32.85 equality reigns
\n" ); document.write( ":
\n" ); document.write( "Did this make sense to you? Did it help? Any question?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );