document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1142738>Question 1142738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company has an order for 810 suits, another company has to make 900 suits in the same period of time. The first company has completed its task 3 days ahead of time and the second company 6 days ahead of time. How many suits does each company produce per day, if the second company makes 4 suits per day more than the first?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #763470 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=763470\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i get the following.\r<BR>\n" );
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document.write( "we have company A and company B.\r<BR>\n" );
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document.write( "company A has an order for 810 suits.<BR>\n" );
document.write( "company B has an order for 900 suits in the same period of time.\r<BR>\n" );
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document.write( "company A completes its task 3 days ahead of time.<BR>\n" );
document.write( "company B completes its task 7 days ahead of time.\r<BR>\n" );
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document.write( "company B make 4 more suits per day than company A.\r<BR>\n" );
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document.write( "the general formula to use is R * T = Q\r<BR>\n" );
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document.write( "R is the number of suits produced per day.<BR>\n" );
document.write( "T is the number of days.<BR>\n" );
document.write( "Q is the number of suits produced.\r<BR>\n" );
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document.write( "for company A, the formula becomes R * (T-3) = 810<BR>\n" );
document.write( "for company B, the formula becomes (R+4) * (T-6) = 900\r<BR>\n" );
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document.write( "solve for R in the first equation to get R = 810/(T-3)\r<BR>\n" );
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document.write( "replace R in the second equation by 810/(T-3) to get:<BR>\n" );
document.write( "(810/(T-3))+4) * (T-6) = 900<BR>\n" );
document.write( "multiply both sides of this equation by (T-3) to get:<BR>\n" );
document.write( "(810 + 4 * (T-3)) * (T-6) = 900 * (T-3)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "(810 + 4*T - 12) * (T - 6) = 900*T - 2700<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "(798 + 4*T) * (T - 6) = 900*T - 2700<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "798*T - 4788 + 4*T^2 - 24*T = 900*T - 2700<BR>\n" );
document.write( "subtract 900*T from both sides of the equation and add 2700 to both sides of the equation and order the terms in descending order of degree to get:<BR>\n" );
document.write( "4*T^2 - 126*% - 2088 = 0<BR>\n" );
document.write( "factor this quadratic equation to get:<BR>\n" );
document.write( "T = 43.5 or T = -12\r<BR>\n" );
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document.write( "T has to be positive so T = 43.5<BR>\n" );
document.write( "since R = 810 / (T-3), you get:<BR>\n" );
document.write( "R = 20\r<BR>\n" );
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document.write( "your solution appears to be that company A produces 20 suits per day and company B produces 24 suits per day.\r<BR>\n" );
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document.write( "company A finishes 3 days ahead of time, so company A finishes in 40.5 days.<BR>\n" );
document.write( "company B finishes 6 days ahead of time, so company B finishes in 37.5 days.\r<BR>\n" );
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document.write( "20 * 40.5 = 810<BR>\n" );
document.write( "24 * 37.5 = 900\r<BR>\n" );
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document.write( "the numbers check out so it appears the solution is good.\r<BR>\n" );
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document.write( "the solution is that company A produces 20 suits per day and company B produces 24 suits per day. </SPAN>\n" );
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