document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084634>Question 1084634</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company had 20 inch and 30 inch televisions is the ratio 4:7. <BR>\n" );
document.write( "100 20 inch TVs were sold and 550 30 inch TVs were sold. <BR>\n" );
document.write( "Their ratio is now 1:1.<BR>\n" );
document.write( "How many TVs did the company start with </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698703 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=698703\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = the number of 20 inch televisions they had to start with.<BR>\n" );
document.write( "let y = the number of 30 inch televisions they had to start with.\r<BR>\n" );
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document.write( "the ratio of 20 inch televisions to 30 inch televisions was 4/7.\r<BR>\n" );
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document.write( "x/y = 4/7\r<BR>\n" );
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document.write( "they sold 100 twenty inch televisions and 550 thirty inch televisions.\r<BR>\n" );
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document.write( "the ratio of 20 inch televisions to 30 inch televisions is now 1/1.\r<BR>\n" );
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document.write( "(x-100) / (y - 550) = 1/1\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 7y to get:\r<BR>\n" );
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document.write( "7x = 4y\r<BR>\n" );
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document.write( "subtract 4y from both sides of the equation to get 7x - 4y = 0\r<BR>\n" );
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document.write( "multiply both sides of the second equation by (y - 550) to get:\r<BR>\n" );
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document.write( "(x - 100) = (y - 550)\r<BR>\n" );
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document.write( "remove parentheses to get:\r<BR>\n" );
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document.write( "x - 100 = y - 550\r<BR>\n" );
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document.write( "add 100 to both sides of this equation and subtract y from both sides of this equation to get:\r<BR>\n" );
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document.write( "x - y = -450\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "7x - 4y = 0\r<BR>\n" );
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document.write( "x - y = -450\r<BR>\n" );
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document.write( "leave the first equation as is and multiply both sides of the second equation by 4 to get:\r<BR>\n" );
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document.write( "7x - 4y = 0<BR>\n" );
document.write( "4x - 4y = -1800\r<BR>\n" );
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document.write( "subtract the second equation from the first to get:\r<BR>\n" );
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document.write( "3x = 1800\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 600\r<BR>\n" );
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document.write( "your original ratio is x/y = 4/7\r<BR>\n" );
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document.write( "when x = 600, this ratio becomes 600/y = 4/7\r<BR>\n" );
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document.write( "cross multiply to get 4y = 4200\r<BR>\n" );
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document.write( "solve for y to get y = 4200/4 = 1050\r<BR>\n" );
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document.write( "you have x = 600 and y = 1050\r<BR>\n" );
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document.write( "x/y = 600/1050 = 4/7\r<BR>\n" );
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document.write( "(x-100) / (y - 550) = (600 - 100) / (1050 - 550) = 500 / 500 = 1/1\r<BR>\n" );
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document.write( "these agree with the problem statements which confirms the solution is correct.\r<BR>\n" );
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document.write( "the solution is:\r<BR>\n" );
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document.write( "number of 20 inch televisions was originally 600 and number of 30 inch televisions was 1050.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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