document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=194419>Question 194419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The manager of a discount store received two clothing shipments.  The first shipment contained 10 sweaters and 20 jackets and cost $800.  The second shipment, at the same prices, contained 5 sweaters and 15 jackets and costs $550.  Find the cost of 1 jacket </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145905 by </B><A HREF=/tutors/aboutme.mpl?userid=doukungfoo><B>doukungfoo(195)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=doukungfoo><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=doukungfoo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=145905\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Lets start out by defining some variables. <BR>\n" );
document.write( "we will call the price of the sweaters x<BR>\n" );
document.write( "and the price of the jackets y<BR>\n" );
document.write( "We are told that 10 sweaters and 20 jackets and cost $800<BR>\n" );
document.write( "write this as an equation using the variables x and y<BR>\n" );
document.write( "10x + 20y = 800\r<BR>\n" );
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document.write( "Now the next part of the problem tells us that 5 sweaters and 15 jackets and costs $550. So write this as an equation:<BR>\n" );
document.write( "5x + 15y = 550\r<BR>\n" );
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document.write( "Ok so we have a system of equations <BR>\n" );
document.write( "10x + 20y = 800<BR>\n" );
document.write( "5x + 15y = 550\r<BR>\n" );
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document.write( "The problem ask us to find the cost of 1 jacket. We stated in the beginning that the price of a jacket is equal to y. So we need to solve for y.<BR>\n" );
document.write( "start with the first equation and set it equal to x<BR>\n" );
document.write( "10x + 20y = 800<BR>\n" );
document.write( "10x = 800 -20y  'subtract 20y from both sides<BR>\n" );
document.write( "x = 80 - 2y 'divide both sides by 10<BR>\n" );
document.write( "Now since we have shown that x is equal to 80 - 2y we can substitute the x in the second equation with 80 - 2y\r<BR>\n" );
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document.write( "5x + 15y = 550<BR>\n" );
document.write( "5(80 - 2y) + 15y = 550 'replace x with 80 - 2y<BR>\n" );
document.write( "400 - 10y + 15y = 550 ' multiply 5 times 80 -2y<BR>\n" );
document.write( "-10y + 15y = 150 'subtract 400 from both sides<BR>\n" );
document.write( "5y = 150 'combine like terms<BR>\n" );
document.write( "y = 30 'divide both sides by 5\r<BR>\n" );
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document.write( "so the cost of 1 jacket is $30.00 </SPAN>\n" );
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