document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168690>Question 1168690</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
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document.write( "Peter was given a  box of pens. He sold all the pens. Each pen was sold at $8.90. For every set of 5 pens sold a pen was given free. 2/3 of the pens were sold in sets of 5 pens. He collected $1174.80 how many pens were in the box at first.<BR>\n" );
document.write( "Thanks\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793317 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = number of pens sold separately.<BR>\n" );
document.write( "y = number of pens sold in sets of 5.<BR>\n" );
document.write( "when the pens are sold separately, they cost 8.90 each.<BR>\n" );
document.write( "when the pens are sold in sets of 5, they cost 44.50 plus the buyer gets a pen for free.<BR>\n" );
document.write( "your cost equation is 8.90 * x + 44.50 * y = 1174.80.<BR>\n" );
document.write( "8.90 is the cost for one pen sold separately.<BR>\n" );
document.write( "44.50 is the cost of a set of 5 pens with 1 extra pen given for free.<BR>\n" );
document.write( "you are given that 2/3 of the pens were sold in sets of 5.<BR>\n" );
document.write( "since (x + y) is the total number of pens sold, this means that y = 2/3 * (x + y)<BR>\n" );
document.write( "simplify to get y = 2/3 * x + 2/3 * y<BR>\n" );
document.write( "subtract 2/3 * y from both sides of this equation to get:<BR>\n" );
document.write( "y - 2/3 * y = 2/3 * x<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "1/3 * y = 2/3 * x<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 3/1 * 2/3 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "y = 2 * x<BR>\n" );
document.write( "in the equation of 8.90 * x + 44.50 * y = 1174.80, replace y with 2 * x to get:<BR>\n" );
document.write( "8.90 * x + 44.50 * 2 * x = 1174.80.<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "8.90 * x + 89 * x = 1174.80<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "97.90 * x = 1174.80<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 12.<BR>\n" );
document.write( "since y = 2 * x, then you get:<BR>\n" );
document.write( "y = 24.<BR>\n" );
document.write( "your equation of 8.90 * x + 44.50 * y = 1174.80 becomes:<BR>\n" );
document.write( "8.90 * 12 + 44.50 * 24 = 1174.80 which becomes 1174.80 = 1174.80, confirming the values of x and y are good.<BR>\n" );
document.write( "x represents 1 pen.<BR>\n" );
document.write( "y represents 6 pens (5 that are bought and 1 that is given free).<BR>\n" );
document.write( "12 * 1 + 24 * 6 = 156.<BR>\n" );
document.write( "there must have been 156 pens in the box.<BR>\n" );
document.write( "that's your solution, as best i can determine.<BR>\n" );
document.write( "he sold 12 pens separately.<BR>\n" );
document.write( "he sold 24 sets of 5 pens each = 120 pens<BR>\n" );
document.write( "he gave away 24 pens (1 for each set of 5).<BR>\n" );
document.write( "the total pens in the box had to be 12 + 120 + 24 = 156.<BR>\n" );
document.write( "132 of the pens were sold.<BR>\n" );
document.write( "24 were given away.\r<BR>\n" );
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