document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201507>Question 1201507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of Karen's beads to Sarah's beads is 7:5 . When Sarah gives 48 beads to Karen, she has 1/3 of the number of beads Karen has. During a game, Karen lost some beads to Sarah. As a result, Karen had 1/5 as many beads as Sarah. How many beads did Karen lose?        </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835907 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=835907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The problem is poorly worded, leading to two different interpretations and thus two different answers.<br><BR>\n" );
document.write( "The other tutor interpreted the problem as meaning that the ratio of Karen's to Sarah's beads was 7:5 before Karen lost some to Sarah.  Another possible interpretation is that Karen lost some to Sarah AFTER Sarah gave 48 of her beads to Karen.<br><BR>\n" );
document.write( "The other tutor showed a solution with his interpretation; here is a solution using the other interpretation.<br><BR>\n" );
document.write( "Originally Karen had 7x beads and Sarah had 5x beads; the total number of beads is 12x.<br><BR>\n" );
document.write( "After Sarah gave 48 beads to Karen, Sarah had 1/3 as many beads as Karen.  Since the total number of beads is 12x, that means Sarah now has 3x beads and Karen has 9x beads.<br><BR>\n" );
document.write( "So the number of beads Sarah gave to Karen, 48, is the difference between 7x and 9x (or the difference between 5x and 3x), which is 2x.  So 2x = 48, x = 24, and the numbers of beads they started with was<br><BR>\n" );
document.write( "Karen: 7x = 168<BR>\n" );
document.write( "Sarah: 5x = 120<br><BR>\n" );
document.write( "And after Sarah gives 48 = 2x beads to Karen, the numbers of beads they have was<br><BR>\n" );
document.write( "Karen: 7x+2x = 9x = 216<BR>\n" );
document.write( "Sarah: 5x-2x = 3x = 72<br><BR>\n" );
document.write( "In the end, since Karen finished with 1/5 as many beads as Sarah, and since the total number of beads was 12x, Karen finished with 2x = 48 beads and Sarah finished with 10x = 240 beads.<br><BR>\n" );
document.write( "So with this interpretation of the problem, the number of beads Karen lost to Sarah was the difference between 9x and 2x (or the difference between 3x and 10x), which is 7x = 168.<br><BR>\n" );
document.write( "Second ANSWER: Karen lost 168 beads to Sarah.<br><BR>\n" );
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