document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184054>Question 1184054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ken had 1 1/2 times as many bookmarks as Lionel. Mike had 3/4 as many bookmarks as <BR>\n" );
document.write( "Ken. Ken and Lionel gave Mike a number of bookmarks in the ratio 3:1. As a result, Mike <BR>\n" );
document.write( "had twice as many bookmarks as before, and Lionel had 32 bookmarks more than Ken. <BR>\n" );
document.write( "How many bookmarks did Ken give to Mike?<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 #838058 by </B><A HREF=/tutors/aboutme.mpl?userid=papachick24025><B>papachick24025(6)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=papachick24025><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=838058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From the first sentence of the problem, we know that: \r<BR>\n" );
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document.write( "K = (3/2)L \r<BR>\n" );
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document.write( "From the second sentence of the problem, we know that: \r<BR>\n" );
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document.write( "M = (3/4)K \r<BR>\n" );
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document.write( "From the third sentence of the problem, we know that: \r<BR>\n" );
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document.write( "k gave m 3x bookmarks and l gave m x bookmarks. Therefore, \r<BR>\n" );
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document.write( "M + 4x = 2(M) \r<BR>\n" );
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document.write( "Simplifying this equation gives us: \r<BR>\n" );
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document.write( "M = 4x \r<BR>\n" );
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document.write( "We also know from the last sentence of the problem that: \r<BR>\n" );
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document.write( "L = K + 32 \r<BR>\n" );
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document.write( "Now we can substitute our expressions for K and M in terms of L into our equation for M: \r<BR>\n" );
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document.write( "(3/4)(3/2)L + 4x = 8x \r<BR>\n" );
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document.write( "Simplifying this equation gives us: \r<BR>\n" );
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document.write( "9L/8 + 4x = 8x \r<BR>\n" );
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document.write( "9L/8 = 4x \r<BR>\n" );
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document.write( "L = (32/9)x \r<BR>\n" );
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document.write( "Substituting this expression for L into our equation for K gives us: \r<BR>\n" );
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document.write( "K = (3/2)(32/9)x = (16/3)x \r<BR>\n" );
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document.write( "Finally, we can substitute our expressions for K and M in terms of x into our equation for M: \r<BR>\n" );
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document.write( "M = (3/4)(16/3)x = 4x \r<BR>\n" );
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document.write( "Therefore, k gave m 3x bookmarks, and since m ended up with 4x bookmarks in total, we have: \r<BR>\n" );
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document.write( "3x + x = 4x \r<BR>\n" );
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document.write( "Solving for x gives us: \r<BR>\n" );
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document.write( "x = 144 \r<BR>\n" );
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document.write( "Therefore, k gave m 3x = 432 bookmarks.  </SPAN>\n" );
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