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 #838062 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The solution from the other (new) tutor is fine.... But it involves a lot of computations with \"ugly\" fractions.<br><BR>\n" );
document.write( "Since there are many different paths to the solution to the problem, let's try something different and see if we find an easier path to the solution.<br><BR>\n" );
document.write( "When the statement of the problem gives ratios, it is often easiest to set up the problem using those ratios.<br><BR>\n" );
document.write( "In this problem, we have...<BR>\n" );
document.write( "(1) K:L = 3:2<BR>\n" );
document.write( "(2) M:K = 3:4<br><BR>\n" );
document.write( "We can use a single variable to solve the problem by finding the ratio M:K:L.  Do that by multiplying each of the given ratios by a constant so that the \"K\" in both ratios is the same number.<BR>\n" );
document.write( "(1) K:L = 3:2 = 12:8<BR>\n" );
document.write( "(2) M:K = 3:4 = 9:12<BR>\n" );
document.write( "(3) M:K:L = 9:12:8<br><BR>\n" );
document.write( "Having done that manipulation with the given ratios...<BR>\n" );
document.write( "Let 9x = number Mike starts with<BR>\n" );
document.write( "Let 12x = number Ken starts with<BR>\n" );
document.write( "Let 8x = number Lionel starts with<br><BR>\n" );
document.write( "Mike ends up with twice as many as he had to start, so<BR>\n" );
document.write( "18x = number Mike ends with<br><BR>\n" );
document.write( "Between them, the number Ken and Lionel gave Mike was 9x.  Ken gave Mike 3 times as many as Lionel gave, so Ken gave Mike 3/4 of the 9x and Lionel gave Mike 1/4 of the 9x:<BR>\n" );
document.write( "(3/4)9x = (27/4)x = number Ken gave Mike<BR>\n" );
document.write( "(1/4)9x = (9/4)x = number Lionel gave Mike<br><BR>\n" );
document.write( "Then...<BR>\n" );
document.write( "the number Ken ends up with is 12x-(27/4)x = (21/4)x<BR>\n" );
document.write( "the number Lionel ends up with is 8x-(9/4)x = (23/4)x<br><BR>\n" );
document.write( "Lionel ends up with 32 more than Ken:<BR>\n" );
document.write( "(23/4)x-(21/4)x = 32<BR>\n" );
document.write( "(2/4)x = (1/2)x = 32<BR>\n" );
document.write( "x = 64<br><BR>\n" );
document.write( "We could figure out all the numbers in the problem -- the numbers each of them started with and the numbers each of them ended with.  But the problem only asks for the number Ken gave to Mike.  That number is<br><BR>\n" );
document.write( "(27/4)x = (27/4)(64) = 27*16 = 432<br><BR>\n" );
document.write( "ANSWER: 432<br><BR>\n" );
document.write( "If this forum works the way it is supposed to, you will get another response or two showing still different ways to set up and solve the problem.<br><BR>\n" );
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