document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333541>Question 333541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The revenue achieved by selling x graphing calculators is figured to be <BR>\n" );
document.write( "x(45-0.5x)dollars. The cost of each calculator is $25. How many graphing calculators must be sold to make a profit(revenue-cost) of at least 187.50?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #239082 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=239082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let r=revenue<BR>\n" );
document.write( "let c=cost<BR>\n" );
document.write( "let p=profit<BR>\n" );
document.write( "let x=number of graphing calculators<BR>\n" );
document.write( "---<BR>\n" );
document.write( "given<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=x%2845-0.5x%29=45x-0.5%2Ax%5E2 ALIGN=MIDDLE  ALT=\"r=x%2845-0.5x%29=45x-0.5%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c=25x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=r-c=45x-0.5%2Ax%5E2-25x ALIGN=MIDDLE  ALT=\"p=r-c=45x-0.5%2Ax%5E2-25x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplify p:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-0.5%2Ax%5E2%2B20x ALIGN=MIDDLE  ALT=\"p=-0.5%2Ax%5E2%2B20x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "need to find x, such that p>187.50<BR>\n" );
document.write( "==<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5%2Ax%5E2%2B20x%3E187.5 ALIGN=MIDDLE  ALT=\"-0.5%2Ax%5E2%2B20x%3E187.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5%2Ax%5E2%2B20x-187.5%3E0 ALIGN=MIDDLE  ALT=\"-0.5%2Ax%5E2%2B20x-187.5%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (subtract 187.50 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B40x-375%3E0+ ALIGN=MIDDLE  ALT=\"-x%5E2%2B40x-375%3E0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (multiply both sides by 2)<BR>\n" );
document.write( "--<BR>\n" );
document.write( "solve via quadratic solution for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-40-sqrt%28%28-40%29%5E2-4%2A%28-1%29%2A%28-375%29%29%29%2F%282%2A%28-1%29%29 ALIGN=MIDDLE  ALT=\"x=%28-40-sqrt%28%28-40%29%5E2-4%2A%28-1%29%2A%28-375%29%29%29%2F%282%2A%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-40%2Bsqrt%28%28-40%29%5E2-4%2A%28-1%29%2A%28-375%29%29%29%2F%282%2A%28-1%29%29 ALIGN=MIDDLE  ALT=\"x=%28-40%2Bsqrt%28%28-40%29%5E2-4%2A%28-1%29%2A%28-375%29%29%29%2F%282%2A%28-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "x=15 or 25  but you need to check for \"valid\" values<BR>\n" );
document.write( "---<BR>\n" );
document.write( "draw a line<BR>\n" );
document.write( "mark the points 15 and 25 on this line<BR>\n" );
document.write( "you have created 3 number segments to check for validity of the x values<BR>\n" );
document.write( "1. x values from -infinity to 15<BR>\n" );
document.write( "2. x values from 15 to 25<BR>\n" );
document.write( "3. x values from 25 to + infinity<BR>\n" );
document.write( "--<BR>\n" );
document.write( "choose a value from each segment, such as 0 for the first segment, 20 for the second segment, and 30 for the third segment. <BR>\n" );
document.write( "test these chosen x values against <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.5%2Ax%5E2%2B20x-187.5%3E0 ALIGN=MIDDLE  ALT=\"-0.5%2Ax%5E2%2B20x-187.5%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to determine the validity of each segment.<BR>\n" );
document.write( "--<BR>\n" );
document.write( "you will find that the line segment for x between 15 to 25 that make the profit positive, and that is your answer (between 15 to 25 calculators will yield a proift greater than 187.50)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );