document.write( "Question 1151555: A sporting goods store sells 90 fishing rods in a season for $200 each. Each $10 decrease in price would result in five more rods being sold. Calculate the number of rods sold and the selling price to generate a revenue of $17 600 from sales of fishing rods. \n" ); document.write( "

Algebra.Com's Answer #773339 by ikleyn(52817) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "According to the condition, the number of rods sold as a function of price \"p\" is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    n(p) = 90 + ,   \r\n" );
document.write( "\r\n" );
document.write( "or, equivalently,\r\n" );
document.write( "\r\n" );
document.write( "    n(p) = 90 + 0.5*(200-p).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The revenue R(p)  as the function of price is then the product\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    R(p) = p*n(p) = p*(90 + 0.5*(200-p) = p*(90 + 100 - 0.5*p) = -0.5p^2 + 190p.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To generate the revenue of 17600 dollars, the price should satisfy this equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    R(p) = 17600 dollars,\r\n" );
document.write( "\r\n" );
document.write( "or, equivalently\r\n" );
document.write( "\r\n" );
document.write( "    -0.5p^2 + 190p = 17600.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and solve for p.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    p^2 - 380p + 35200 = 0\r\n" );
document.write( "\r\n" );
document.write( "     =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  There are two solutions: p= 160  and  p= 220  dollars.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );