document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184398>Question 1184398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Andy can buy 3 mechanical pencils with 2/7 of his money. He can buy 6 mechanical pencils and 3 pens with the rest of his money. If he only buys pens, how many pens can he buy with all his money? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814987 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=814987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> m = price of a mechanical pencil.<BR>\n" );
document.write( "p = price of a pen.\r<BR>\n" );
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document.write( "3m = 2/7 * x.<BR>\n" );
document.write( "6m + 3p = 5/7 * x.<BR>\n" );
document.write( "5/7 * x = the rest of his money after he spent 2/7 * x.<BR>\n" );
document.write( "if 3m = 2/7 * x, then 6m = 4/7 * x.<BR>\n" );
document.write( "6m + 3p = 5/7 * x becomes 4/7 * x + 3p = 5/7 * x.<BR>\n" );
document.write( "subtract 4/7 * x from both sides of this equation to get 3p = 1/7 * x.<BR>\n" );
document.write( "solve for p to get p = 1/21 * x.<BR>\n" );
document.write( "solve for x to get x = 21 * p.\r<BR>\n" );
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document.write( "that's your answer.<BR>\n" );
document.write( "he could buy 21 pens with his original amount of money.\r<BR>\n" );
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document.write( "to confirm, replace x with any value of money.<BR>\n" );
document.write( "i chose 105 dollars because that's a multiple of 7 (105 / 7 = 15).<BR>\n" );
document.write( "when x = 105, he could buy 3 mechanical pencils with 2/7 of his money.<BR>\n" );
document.write( "that means he could buy 3 mechanical pencils for 30 dollars.<BR>\n" );
document.write( "that means each mechanical pencil costs 10 dollars.<BR>\n" );
document.write( "he could also buy 6 mechanical pencils and 3 pens for 5/7 times 105.<BR>\n" );
document.write( "5/7 times 105 = 75 dollars.<BR>\n" );
document.write( "6 mechanical pencils cost 60 dollars, leaving 15 dollars for the pens.<BR>\n" );
document.write( "3 pens for 15 dollars means that each pen costs 5 dollars.<BR>\n" );
document.write( "105 / 5 = 21 pens that can be bought for 105 dollars at 5 dollars apiece.\r<BR>\n" );
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document.write( "you get the same answer whether you're working with x or with some value for x.<BR>\n" );
document.write( "this is as it should be.<BR>\n" );
document.write( "the answer for x is confirmed when i used  value for x instead.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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