document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203331>Question 1203331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Betty baked some cheese buns and butter buns. After she sold 1/3 of the cheese buns and 2/5 of the butter buns, she had 50% as many butter buns as cheese buns left. What fraction of the buns baked was butter buns? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838801 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=838801\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I thought of several different ways to attack this problem and couldn't decide easily which one would be easier, so I tried different ones.<br><BR>\n" );
document.write( "That in itself is a good lesson in problem solving, whether it is a math problem or a problem in real life.  Always be open to trying different ways of doing things. If we didn't do that, we would all still be living in caves.<br><BR>\n" );
document.write( "Method 1...<br><BR>\n" );
document.write( "let b = # of butter buns<BR>\n" );
document.write( "let c = # of cheese buns<br><BR>\n" );
document.write( "The number we are to find is the fraction of the buns that are butter buns.  That fraction is b/(b+c).<br><BR>\n" );
document.write( "She sold 1/3 of the cheese buns, so the number she had left was (2/3)c.<br><BR>\n" );
document.write( "She sold 2/5 of the butter buns, so the number she had left was (3/5)b.<br><BR>\n" );
document.write( "The number of butter buns she had left was half the number of cheese buns; i.e., the number of cheese buns she had left was twice the number of butter buns.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29c=2%28%283%2F5%29b%29 ALIGN=MIDDLE  ALT=\"%282%2F3%29c=2%28%283%2F5%29b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10c=18b ALIGN=MIDDLE  ALT=\"10c=18b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Fc=10%2F18=5%2F9 ALIGN=MIDDLE  ALT=\"b%2Fc=10%2F18=5%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F%28b%2Bc%29=5%2F%285%2B9%29=5%2F14 ALIGN=MIDDLE  ALT=\"b%2F%28b%2Bc%29=5%2F%285%2B9%29=5%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 5/14<br><BR>\n" );
document.write( "Method 2...<br><BR>\n" );
document.write( "let x = # of butter buns she had left<BR>\n" );
document.write( "then 2x= # of cheese buns she had left<br><BR>\n" );
document.write( "She sold 1/3 of the cheese buns, so she was left with 2/3 of them.  She was left with 2x cheese buns, so the number she started with was (3/2)(2x) = 3x.<br><BR>\n" );
document.write( "She sold 2/5 of the butter buns, so she was left with 3/5 of them. She was left with x butter buns, so the number she started with was (5/3)x.<br><BR>\n" );
document.write( "She started with (5/3)x butter buns and 3x cheese buns.  The fraction of buns that were butter buns was<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285%2F3%29x%29%2F%28%285%2F3%29x%2B3x%29=5x%2F%285x%2B9x%29=%285x%29%2F%2814x%29=5%2F14 ALIGN=MIDDLE  ALT=\"%28%285%2F3%29x%29%2F%28%285%2F3%29x%2B3x%29=5x%2F%285x%2B9x%29=%285x%29%2F%2814x%29=5%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 5/14<br><BR>\n" );
document.write( "Method 3...<br><BR>\n" );
document.write( "let x = fraction of the buns that were butter buns<BR>\n" );
document.write( "then 1-x = fraction that were cheese buns<br><BR>\n" );
document.write( "She was left with (3/5)x butter buns and (2/3)(1-x) cheese buns; and the number of cheese buns left was twice the number of butter buns left:<br><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%281-x%29=18x ALIGN=MIDDLE  ALT=\"10%281-x%29=18x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=28x ALIGN=MIDDLE  ALT=\"10=28x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F14 ALIGN=MIDDLE  ALT=\"x=5%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 5/14<br><BR>\n" );
document.write( "Having solved the problem three different ways, I see tricky parts in each of the methods, so I don't have a strong preference for any one of them....<br><BR>\n" );
document.write( "Perhaps another tutor will present a different method for solving the problem that is easier than any of the above.<br><BR>\n" );
document.write( " </SPAN>\n" );
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