document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=30901>Question 30901</A>: <I><SPAN STYLE=\"word-break: break-all;\"> heres another word problem:  a clothing manufacturer purchased 100 yds of cotton and 50 yds of wool for a total cost of $125. Another purchase, at the same prices, included 70 yds of cotton and 40 yds of wool for a total cost of $90.Find the cost per yard of the cotton and wool. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #17702 by </B><A HREF=/tutors/aboutme.mpl?userid=blubunny01><B>blubunny01(20)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=blubunny01><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=17702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem asks you to find two unknowns: cost/yard of cotton, and cost/yard of wool.\r<BR>\n" );
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document.write( "Let x = cost/yard of cotton.<BR>\n" );
document.write( "Let y = cost/yard of wool.\r<BR>\n" );
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document.write( "We know that a clothing manufacturer purchased 100 yds of cotton and 50 yds of wool for a total cost of $125.  So, to put this into an equation, we have:<BR>\n" );
document.write( "100x + 50y = 125.\r<BR>\n" );
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document.write( "We also know that a purchase was made for 70 yds of cotton and 40 yds of wool for a total cost of $90.  Again, to put this into an equation, we have:<BR>\n" );
document.write( "70x + 40y = 90.\r<BR>\n" );
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document.write( "Now you have two equations for two unknowns, and there are several ways to solve these types of problems.  For simplicity, I'll use the substitution method.\r<BR>\n" );
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document.write( "I'll take 100x + 50y = 125 and solve for x:<BR>\n" );
document.write( "100x = 125 - 50y<BR>\n" );
document.write( "   x = (125/100) - (50/100)y<BR>\n" );
document.write( "   x = (5/4) - (1/2)y\r<BR>\n" );
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document.write( "Then I'll substitute it into the second equation, 70x + 40y = 90.<BR>\n" );
document.write( "70[(5/4) - (1/2)y] + 40y = 90.  \r<BR>\n" );
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document.write( "Now, I can solve for y.\r<BR>\n" );
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document.write( "70[(5/4) - (1/2)y] + 40y = 90.  \r<BR>\n" );
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document.write( "[87.5 - 35y] + 40y = 90\r<BR>\n" );
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document.write( "87.5 + 5y = 90\r<BR>\n" );
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document.write( "5y = 2.5<BR>\n" );
document.write( "y = 0.5\r<BR>\n" );
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document.write( "Now, we can go back to the previous equation and solve for x:<BR>\n" );
document.write( "x = (5/4) - (1/2)y<BR>\n" );
document.write( "x = (5/4) - (1/2)(0.5)<BR>\n" );
document.write( "x = (5/4) - (1/4)<BR>\n" );
document.write( "x = 1\r<BR>\n" );
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document.write( "This means, the cost of cotton is $1.00, and the cost of wool is $0.50. </SPAN>\n" );
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