document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153236>Question 153236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The manager at Cream of the Crop bought a load of watermelons for $200.  She priced the melons so that she would make $1.50 profit for each melon.  When all but 30 had been sold, the manager had recovered her initial investment.  How many did she buy originally? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112776 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=112776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The manager at Cream of the Crop bought a load of watermelons for $200. She priced the melons so that she would make $1.50 profit for each melon. When all but 30 had been sold, the manager had recovered her initial investment. How many did she buy originally?<BR>\n" );
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document.write( "Let the original number bought be \"x\".<BR>\n" );
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document.write( "Average cost of each melon was $(200/x)<BR>\n" );
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document.write( "She priced the melons so that she would make $1.50 profit for each melon.<BR>\n" );
document.write( "Let her price per melon be \"p\".<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "p = (200/x) + 1.5<BR>\n" );
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document.write( "When all but 30 had been sold, the manager had recovered her initial investment.<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "p(x-30) = 200<BR>\n" );
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document.write( "Rearrange the two equations:<BR>\n" );
document.write( "p = (200/x) + 1.5<BR>\n" );
document.write( "p = 200/(x-30)<BR>\n" );
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document.write( "Substitute to solve for \"x\".<BR>\n" );
document.write( "200/(x-30) = (200/x) + 1.5<BR>\n" );
document.write( "Multiply thru by x(x-30) to get:<BR>\n" );
document.write( "200x = 200(x-30) + 1.5x(x-30)<BR>\n" );
document.write( "6000 = 1.5x^2 - 45x<BR>\n" );
document.write( "x^2 - 30x -4000 = 0<BR>\n" );
document.write( "(x- 80)(x+50) = 0<BR>\n" );
document.write( "Positive solution<BR>\n" );
document.write( "x = 80 (original number of melons)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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