document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=484827>Question 484827</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cook used all of a 2-pound chunk of cheese in making three recipes.  Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe III.\r<BR>\n" );
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document.write( "a. What part of the whole chunk of cheese, and how many pounds, did each recipe use?\r<BR>\n" );
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document.write( "b. If the whole chunk of cheese cost $6.60, how much was the cheese in each recipe worth.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #331701 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=331701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A cook used all of a 2-pound chunk of cheese in making three recipes.  Recipe I used one-third as much cheese as Recipe II did, and Recipe II used one-half as much cheese as Recipe III.\r<BR>\n" );
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document.write( "a. What part of the whole chunk of cheese, and how many pounds, did each recipe use?\r<BR>\n" );
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document.write( "b. If the whole chunk of cheese cost $6.60, how much was the cheese in each recipe worth. <BR>\n" );
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document.write( "a.<BR>\n" );
document.write( "Let a = the amount of cheese in recipe I.<BR>\n" );
document.write( "Let b = the amount in recipe II.<BR>\n" );
document.write( "Then the amount in recipe III = 2 - a - b<BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "I used 1/3 as much as II.<BR>\n" );
document.write( "a = b/3 [1]<BR>\n" );
document.write( "II used one-half as much as III.<BR>\n" );
document.write( "b = 1/2(2 - a - b) [2]<BR>\n" );
document.write( "Use the value for a in [1] into [2]:<BR>\n" );
document.write( "b = 1/2(2 - b/3 - b)<BR>\n" );
document.write( "b = 1 - b/6 - b/2<BR>\n" );
document.write( "b = 1 - b/6 - 3b/6<BR>\n" );
document.write( "10b/6 = 1<BR>\n" );
document.write( "b = 6/10 = 3/5<BR>\n" );
document.write( "Therefore a = 3/15 = 1/5<BR>\n" );
document.write( "and recipe III contains 2 - 1/5 - 3/5 = 6/5<BR>\n" );
document.write( "So the amounts are 1/5, 3/5 and 6/5 pounds for recipe I, II and III resp.<BR>\n" );
document.write( "b.<BR>\n" );
document.write( "The cheese costs $6.60/2 lbs = $3.30 per pound<BR>\n" );
document.write( "I: 1/5lb*3.30 = $0.66<BR>\n" );
document.write( "II: 3/5lb*3.30 = $1.98<BR>\n" );
document.write( "III: 6/5lb*6.60 = $3.96  </SPAN>\n" );
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