document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126925>Question 126925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a man purchased a number of balloons, each of the same price, for a total of $720. he sold them all at $40 each, thus realizing a profit equal to his 8 balloons. how many did he buy?\r<BR>\n" );
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document.write( "can you solve this using the quadratic equation??? thanks!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93212 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a man purchased a number of balloons, each of the same price, for a total of $720. he sold them all at $40 each, thus realizing a profit equal to his 8 balloons. how many did he buy?<BR>\n" );
document.write( "can you solve this using the quadratic equation??? thanks!!<BR>\n" );
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document.write( "Let's write down what we know here:<BR>\n" );
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document.write( "Let x = no. of balloons purchased<BR>\n" );
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document.write( "Price he paid for each = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2Fx ALIGN=MIDDLE  ALT=\"720%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Profit given as: 8(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2Fx ALIGN=MIDDLE  ALT=\"720%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "Revenue from the sale of all the balloons = 40x<BR>\n" );
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document.write( "Revenue - cost = profit<BR>\n" );
document.write( "40x - 720 = 8(720/x)<BR>\n" );
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document.write( "40x - 720 = 5760/x<BR>\n" );
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document.write( "40x^2 - 720x = 5760; multiplied equation by x to get rid of the denominator<BR>\n" );
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document.write( "40x^2 - 720x - 5760 = 0 the quadratic equation you so earnestly desired. <BR>\n" );
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document.write( "x^2 - 18x - 144 = 0 simplified, divided equation by 40<BR>\n" );
document.write( "Factor to:<BR>\n" );
document.write( "(x - 24)(x + 6) = 0<BR>\n" );
document.write( "The positive solution is what we want:<BR>\n" );
document.write( "x = 24 balloons<BR>\n" );
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document.write( "His cost for each balloon: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F24 ALIGN=MIDDLE  ALT=\"720%2F24\"   DISABLED_style= \"max-width:90%; height:auto;\" > = $30<BR>\n" );
document.write( "Check solution in the profit equation<BR>\n" );
document.write( "40(24) - 720 = 8(30)<BR>\n" );
document.write( "960 - 720 = 240; confirms our solution<BR>\n" );
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document.write( "How about this? Did it make sense to you? Any questions?<BR>\n" );
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