document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210613>Question 1210613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marek and Zaven had 900 coins altogether. Marek spent 25% fewer coins than Zaven. Zaven was left with 50% as many coins as the number he spent. Marek had 75% of the total number of coins the two friends had left in the end. How many coins did Marek have in the end?<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 #854420 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13351)</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=854420\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "After working a short way through the problem, I chose to set the problem up like this, to make the work easier by avoiding having to work with fractions or decimals.<br><BR>\n" );
document.write( "Marek spent 25% fewer coins than Zaven -- i.e., he spent three-fourths as many as Zaven.  So<br><BR>\n" );
document.write( "Let 4x = # Zaven spent<BR>\n" );
document.write( "Then 3x = # Marek spent<br><BR>\n" );
document.write( "The number Zaven left with was half the number he spent.  So<br><BR>\n" );
document.write( "2x = # Zaven was left with; and then<BR>\n" );
document.write( "4x+2x = 6x = # Zaven started with<br><BR>\n" );
document.write( "The total number of coins the two of them had is 900, so<br><BR>\n" );
document.write( "900-6x = # Marek started with<br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "(90-6x)-3x = 900-9x = # Marek finished with<br><BR>\n" );
document.write( "In the end, Marek had 3/4 of the total number of coins.  Here we have two (at least) ways to continue; we could either say that the number Marek finished with is 3/4 of the total 900, or we could say Marek finished with 3 times as many as Zaven.  For an unknown reason, I chose the second option when I first worked the problem all the way through.<br><BR>\n" );
document.write( "900-9x = 3(2x)<BR>\n" );
document.write( "900-9x = 6x<BR>\n" );
document.write( "900 = 15x<BR>\n" );
document.write( "x = 900/15 = 60<br><BR>\n" );
document.write( "The problem asks for the number Marek finished with.<br><BR>\n" );
document.write( "ANSWER: 900-9x = 900-540 = 360<br><BR>\n" );
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