document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210616>Question 1210616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Emir, Cillian, and Lasha are avid collectors of vintage postage stamps. During a local exhibition, they decided to donate parts of their collections to a museum. The ratio of the number of stamps Emir and Cillian gave away was 4:7, while the ratio of the number of stamps Cillian and Lasha gave away was 3:5. The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself. Cillian kept 3/2 as many stamps as Emir kept, and Lasha kept 4/3 as many stamps as Cillian kept. After their donations, they had a combined total of 738 stamps left in their collections. How many stamps did Lasha give away? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854423 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5362)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854423\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> EDIT: My calculations are wrong. See The much clearer and direct solution by iklein.\r<BR>\n" );
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document.write( "For every 4 stamps donated by Emir, there were 7 stamps donated by Cillian.<BR>\n" );
document.write( "For every 3 stamps donated by Cillian, there were 5 stamps donated by Lasha.<BR>\n" );
document.write( "That means that for every <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2A3=21 ALIGN=MIDDLE  ALT=\"7%2A3=21\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamps given away by Cillian, there were<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A3=12 ALIGN=MIDDLE  ALT=\"4%2A3=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamps given away by Emir, and<BR>\n" );
document.write( "This is wrong --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A3=15 ALIGN=MIDDLE  ALT=\"5%2A3=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamps given away by Lasha.<BR>\n" );
document.write( "It should have been <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A7=35 ALIGN=MIDDLE  ALT=\"5%2A7=35\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "Let us make<BR>\n" );
document.write( "the number of stamps donated by Emir <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x ALIGN=MIDDLE  ALT=\"12x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the number of stamps given by Cillian <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21x ALIGN=MIDDLE  ALT=\"21x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "the number of stamps given by Lasha <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%22=%22 ALIGN=MIDDLE  ALT=\"%22=%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15x ALIGN=MIDDLE  ALT=\"15x\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
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document.write( "EDIT:Here is where the other solutions are better (besides having no mistakes). I insisted on calculating number of stamps kept based on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > , but that unnecessarily complicates the calculations.\r<BR>\n" );
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document.write( "The number of stamps Emir gave away was 20 fewer than the number of stamps he kept for himself means Emir kept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12x%2B20 ALIGN=MIDDLE  ALT=\"12x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamps. See the much clearer and direct solution by Iklein.\r<BR>\n" );
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document.write( "Cillian kept 3/2 as many stamps as Emir, Cillian and Lasha kept means<BR>\n" );
document.write( "Cillian kept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F2%29%2812x%2B20%29=18x%2B30 ALIGN=MIDDLE  ALT=\"%283%2F2%29%2812x%2B20%29=18x%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamps.<BR>\n" );
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document.write( "Lasha kept 4/3 as many stamps as Cillian kept means<BR>\n" );
document.write( "Lasha kept <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29%2818x%2B30%29=24x%2B40 ALIGN=MIDDLE  ALT=\"%284%2F3%29%2818x%2B30%29=24x%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamps.\r<BR>\n" );
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document.write( "After their donations, the total number of stamps Emir, Cillian and Lasha had  left in their collections was<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x%2B20%29%2B%2818x%2B30%29%2B%2824x%2B40%29=738 ALIGN=MIDDLE  ALT=\"%2812x%2B20%29%2B%2818x%2B30%29%2B%2824x%2B40%29=738\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2B18%2B24%29x%2B20%2B30%2B40=738 ALIGN=MIDDLE  ALT=\"%2812%2B18%2B24%29x%2B20%2B30%2B40=738\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54x%2B90=738 ALIGN=MIDDLE  ALT=\"54x%2B90=738\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54x=738-90 ALIGN=MIDDLE  ALT=\"54x=738-90\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54x=648 ALIGN=MIDDLE  ALT=\"54x=648\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=648%2F54 ALIGN=MIDDLE  ALT=\"x=648%2F54\"   DISABLED_style= \"max-width:90%; height:auto;\" >--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Lasha gave away<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A12=highlight%28180%29 ALIGN=MIDDLE  ALT=\"15%2A12=highlight%28180%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > stamps.<BR>\n" );
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document.write( "In table form that looks like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C%22+%22%2CEmir%2CCillian%2C+Lasha%2C%0D%0Ainitial%2C%22%3F%22%2C%22%3F%22%2C%22%3F%22%2C%0D%0Adonated%2C12x%2C21x%2C+15x%2C%0D%0Akept%2C12x%2B20%2C%283%2F2%29%2812x%2B20%29%2C%284%2F3%29%283%2F2%29%2812x%2B20%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C%22+%22%2CEmir%2CCillian%2C+Lasha%2C%0D%0Ainitial%2C%22%3F%22%2C%22%3F%22%2C%22%3F%22%2C%0D%0Adonated%2C12x%2C21x%2C15x%2C%0D%0Akept%2C12x%2B20%2C18x%2B30%2C24x%2B40%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "After solving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812x%2B20%29%2B%2812x%2B20%29%2B%2824x%2B40%29=738 ALIGN=MIDDLE  ALT=\"%2812x%2B20%29%2B%2812x%2B20%29%2B%2824x%2B40%29=738\"   DISABLED_style= \"max-width:90%; height:auto;\" >->->-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=12 ALIGN=MIDDLE  ALT=\"x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we can substitute that value to get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%284%2C4%2C%22+%22%2CEmir%2CCillian%2C+Lasha%2C%0D%0Ainitial%2C%22%3F%22%2C%22%3F%22%2C%22%3F%22%2C%0D%0Adonated%2C12x%2C21x%2C15%2A12%2C%0D%0Akept%2C164%2C246%2C328%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "We can calculate the number of stamps each one originally had, and the number each donated,<BR>\n" );
document.write( "but we are only asked for the number Lasha donated: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2A12=180 ALIGN=MIDDLE  ALT=\"15%2A12=180\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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