document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=125379>Question 125379</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi turor,<BR>\n" );
document.write( "    One more time I going to need your help. Thanks and god bless you.\r<BR>\n" );
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document.write( "1)The golden ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimension would the length and width have the golden ratio?\r<BR>\n" );
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document.write( "2)Work. Henry sold 120 magazine subscriptions in X + 2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week?\r<BR>\n" );
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document.write( "3)Barn painting. Melanie can paint a certain barn by herself in X days. Her helper Melissa can paint the same barn by herself in X days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for  X = 5\r<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 #91884 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91884\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)The golden ratio. The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimension would the length and width have the golden ratio? <BR>\n" );
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document.write( "length/ width = 8/5<BR>\n" );
document.write( "Your Problem:<BR>\n" );
document.write( "Let width be \"x\" ft ; then length is \"x+2\" ft<BR>\n" );
document.write( "(x+2)/x = 8/5<BR>\n" );
document.write( "Cross-multiply to get:<BR>\n" );
document.write( "5x+10 = 8x<BR>\n" );
document.write( "3x = 10<BR>\n" );
document.write( "x = 3 1/3 ft. (width)<BR>\n" );
document.write( "x+2 = 5 1/3 ft. (length)<BR>\n" );
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document.write( "2)Work. Henry sold 120 magazine subscriptions in X + 2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week?<BR>\n" );
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document.write( "On the average he sells 120/(x+2) magazines per day.<BR>\n" );
document.write( "In a week he would sell 7(120/(x+2) = 840/(x+2)<BR>\n" );
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document.write( "Your 2nd sentence makes me think you left something out<BR>\n" );
document.write( "of the problem description.<BR>\n" );
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document.write( "3)Barn painting. Melanie can paint a certain barn by herself in X days. Her helper Melissa can paint the same barn by herself in X days. Write a rational expression for the fraction of the barn that they complete in one day by working together. Evaluate the expression for X = 5 <BR>\n" );
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document.write( "Melanie DATA;<BR>\n" );
document.write( "Time = x days/job : rate = 1/x jobs/day<BR>\n" );
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document.write( "Melissa DATA:<BR>\n" );
document.write( "Time = x days/job ; rate = 1/x jobs/day<BR>\n" );
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document.write( "Together DATA:<BR>\n" );
document.write( "Time = y days/job ; rate = 1/y jobs/day<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "1/x + 1/x = 1/y<BR>\n" );
document.write( "2/x = 1/y <BR>\n" );
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document.write( "Since they do 1/y job/day, they do (2/x) jobs/day<BR>\n" );
document.write( "If x= 5, together they do (2/5) job per day.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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