document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1080325>Question 1080325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A traffic check counted 390 cars passing a certain spot on one day and 430 cars at the same spot of the second day. On the first day, there are three times as many cars going east and half as many going west as on the second day. What was the total number of eastbound cars and the total number of west bound cars for the two days? How many are:<BR>\n" );
document.write( "(a) East? (b) West? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #694490 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=694490\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = number of cars going eastbound<BR>\n" );
document.write( "let y = number of cars going westbound.\r<BR>\n" );
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document.write( "on day 1 you have 3 times as many cars going eastbound as on day 2.<BR>\n" );
document.write( "on day 1 you have 1/2 as many cars going westbound as on day 2.\r<BR>\n" );
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document.write( "draw a table similar to one shown below:\r<BR>\n" );
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document.write( "                        east             west             total\r\n" );
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document.write( "day 1                    3x               y                390\r\n" );
document.write( "day 2                     x              2y                430\r\n" );
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document.write( "total                    4x              3y                820\r\n" );
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document.write( "since 3x is 3 times x, your first requirements is satisfied because 3 times as many cars are going east on day 1 as on day 2.\r<BR>\n" );
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document.write( "since y is 1/2 of 2y, your second requirement is satisfied because 1/2 as many cars are going west on day 1 as on day 2.\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( "3x + y = 390<BR>\n" );
document.write( "x + 2y = 430\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 2 and leave the second equation as is to get:\r<BR>\n" );
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document.write( "6x + 2y = 780<BR>\n" );
document.write( "x + 2y = 430\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( "5x = 350\r<BR>\n" );
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document.write( "solve for x to get x = 530 / 5 = 70\r<BR>\n" );
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document.write( "in the first original equation, solve for y as follows:\r<BR>\n" );
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document.write( "start with 3x + y = 390<BR>\n" );
document.write( "replace x with 70 to get 3*70 + y = 390<BR>\n" );
document.write( "simplify to get 210 + y = 390<BR>\n" );
document.write( "subtract 210 from both sides to get y = 390 - 210<BR>\n" );
document.write( "simplify to get y = 180\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 70<BR>\n" );
document.write( "y = 180\r<BR>\n" );
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document.write( "substitute in both original equation to get:\r<BR>\n" );
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document.write( "3x + y = 390 becomes 3*70 + 180 = 390 which becomes 210 + 180 = 390 which becomes 390 = 390 which is true.\r<BR>\n" );
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document.write( "x + 2y = 430 becomes 70 + 2*180 = 430 which becomes 70 + 360 = 430 which becomes 430 = 430 which is true.\r<BR>\n" );
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document.write( "the solutions look good.\r<BR>\n" );
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document.write( "the question was how many cars were eastbound total and how many cars were westbound total.\r<BR>\n" );
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document.write( "3x + x = 4x = 4*70 = 280<BR>\n" );
document.write( "y + 2y = 180 + 360 = 540\r<BR>\n" );
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document.write( "total cars both ways for both days = 820<BR>\n" );
document.write( "total of 280 were eastbound<BR>\n" );
document.write( "total of 540 were westbound\r<BR>\n" );
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document.write( " </SPAN>\n" );
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