document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=912703>Question 912703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We are learning how to complete the square and I'm having trouble with this question. A student club is planning a fundraising car wash. Last year they charged $10 per vehicle and washed 120 vehicles. They would like to earn more money this year. For every $1 increase in price, they know they will wash 5 fewer vehicles. Determine the best price to charge the car wash and the revenue expected at that price. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #553986 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=553986\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Completing The Square is the easier part of the question.  The tougher part is to derive the function from the description.\r<BR>\n" );
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document.write( "The question focuses on revenue, ignoring cost and profit.\r<BR>\n" );
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document.write( "Let x be the price per car.\r<BR>\n" );
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document.write( "CARS_________PRICE_________REVENUE<BR>\n" );
document.write( "120____________10<BR>\n" );
document.write( "115____________11<BR>\n" );
document.write( "110____________12<BR>\n" );
document.write( "105____________13<BR>\n" );
document.write( "120-5x________10+x_______(120-5x)(10+x)\r<BR>\n" );
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document.write( "The income expected this year will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%28-5x%2B120%29%28x%2B10%29%29 ALIGN=MIDDLE  ALT=\"highlight%28%28-5x%2B120%29%28x%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "If you WANT to do this through Completing the Square, assign the expression as a function and simplify.<BR>\n" );
document.write( "r for revenue:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29=1200-50x%2B120x-5x%5E2 ALIGN=MIDDLE  ALT=\"r%28x%29=1200-50x%2B120x-5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplying the two binomials;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28x%29=-5x%5E2%2B70x%2B1200 ALIGN=MIDDLE  ALT=\"r%28x%29=-5x%5E2%2B70x%2B1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28r%28x%29=-5%28x%5E2-14x-240%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28r%28x%29=-5%28x%5E2-14x-240%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now you have r(x) using r as revenue function, x as the price per car, in general form but showing multiplication by a factor.  Can you Complete the Square for the function and find the vertex?\r<BR>\n" );
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document.write( "These lessons could help regarding Completing the Square:<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"http://www.algebra.com/my/Completing-the-Square-Using-Pictures.lesson?content_action=show_dev\">http://www.algebra.com/my/Completing-the-Square-Using-Pictures.lesson?content_action=show_dev</a><BR>\n" );
document.write( "<a  rel=nofollow HREF=\"http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev\">http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev</a> </SPAN>\n" );
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