document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164615>Question 164615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Manufacturing: a company manufactures both mountain bikes and trail bikes. The cost of materials for a mountain bike is $70, and the cost of materials for a trail bike is $50. The cost of labor to manufacture a mountain bike is $80, and the cost of labor to manufacture a trail bike is $40. During a week in which the company has budgeted $2500 for materials and $2600 for labor, how many mountain bikes does the company plan to manufacture?\r<BR>\n" );
document.write( "\n" );
document.write( "What I need is what steps to take to solve this problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121304 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=121304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of mountain bikes to be manufactured.<BR>\n" );
document.write( "let y = number of trail bikes to be manufactured.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "total cost of material is $2500.<BR>\n" );
document.write( "cost of material for mountain bike is 70.<BR>\n" );
document.write( "cost of material for trail bike is 50.<BR>\n" );
document.write( "equation for total material is:<BR>\n" );
document.write( "70*x + 50*y = 2500<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "total cost of labor is $2600.<BR>\n" );
document.write( "cost of labor for mountain bike is 80.<BR>\n" );
document.write( "cost of labor for trail bike is 40.<BR>\n" );
document.write( "equation for total labor is:<BR>\n" );
document.write( "80*x + 40*y = 2600<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "solve these equations simultaneously.<BR>\n" );
document.write( "70*x + 50*y = 2500 (first equation)<BR>\n" );
document.write( "80*x + 40*y = 2600 (second equation)<BR>\n" );
document.write( "multiply both sides of first equation by 4 and multiply both sides of second equation by 5.  this will allow you to eliminate the y from the equation so you can solve for x.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "280*x + 200*y = 10000<BR>\n" );
document.write( "400*x + 200*y = 13000<BR>\n" );
document.write( "subtract first equation from second equation.<BR>\n" );
document.write( "120*x = 3000<BR>\n" );
document.write( "divide both sides by 120.<BR>\n" );
document.write( "x = 25<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute 25 for x in first equation.<BR>\n" );
document.write( "70*(25) + 50*y = 2500<BR>\n" );
document.write( "1750 + 50*y = 2500<BR>\n" );
document.write( "subtract 1750 from both sides<BR>\n" );
document.write( "50*y = 750<BR>\n" );
document.write( "y = 15<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substitute 25 for x and 15 for y in second equation.<BR>\n" );
document.write( "80*25 + 40*15 = 2600<BR>\n" );
document.write( "2000 + 600 = 2600<BR>\n" );
document.write( "2600 = 2600<BR>\n" );
document.write( "x = 25 and y = 15 are good in second equation.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "x = 25<BR>\n" );
document.write( "y = 15<BR>\n" );
document.write( "number of mountain bikes to manufacture = 25<BR>\n" );
document.write( "number of trail bikes to manufacture = 15<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );