document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=813641>Question 813641</A>: <I><SPAN STYLE=\"word-break: break-all;\">  When a vendor prices key chains at $5 each, she sells 210 key chains. For each $1 she raises the price, she sells 10 fewer key chains. USE AN EQUATION to determine what she should charge to maximize her revenue from sales. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #489855 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=489855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use the revenue equation:<BR>\n" );
document.write( "r = p * n<BR>\n" );
document.write( "where<BR>\n" );
document.write( "p = price per item<BR>\n" );
document.write( "n = number of items sold<BR>\n" );
document.write( "---<BR>\n" );
document.write( "because we know that changing the price (p) also changes the number sold (n), we need to introduce a variable to the revenue equation to measure the changes in p and n.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "so just make up a variable, call it x, such that:<BR>\n" );
document.write( "p + x means a one dollar price increase and<BR>\n" );
document.write( "p - x means a one dollar price decrease and<BR>\n" );
document.write( "n + x means a one item number-sold increase and<BR>\n" );
document.write( "n - x means a one item number-sold decrease<BR>\n" );
document.write( "---<BR>\n" );
document.write( "for each $1 price increase (p + x) there are 10 fewer items sold (n - 10x), so:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "r = (p + x) * (n - 10x)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "we know that at $5 per item, she sells 210 items, so:<BR>\n" );
document.write( "r = (5 + x) * (210 - 10x)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "r = (5 + x) * (210 - 10x)<BR>\n" );
document.write( "r = 1050 - 50x + 210x - 10xx<BR>\n" );
document.write( "r = -10xx + 160x + 1050<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the above quadratic equation is in standard form, with a=-10, b=160, and c=1050<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to solve the quadratic equation, plug this:<BR>\n" );
document.write( "-10 160 1050<BR>\n" );
document.write( "into this: https://sooeet.com/math/quadratic-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Answer 1:<BR>\n" );
document.write( "the quadratic equation has a maximum at: ( x=8, r=1690 ), so:<BR>\n" );
document.write( "maximum revenue is $1690<BR>\n" );
document.write( "when price per item is $8<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Convert fractions, decimals, and percents:<BR>\n" );
document.write( "https://sooeet.com/math/fraction-decimal-percent.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Calculate and graph the linear regression of any data set:<BR>\n" );
document.write( "https://sooeet.com/math/linear-regression.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );