document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=950665>Question 950665</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am not very good with word problems, and my parents can't help me right now because they are busy, but i think i have a start and i was hoping to confirm my structure of solving this question. \r<BR>\n" );
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document.write( "At Happy Burger you can get one order of fries and one burger for $7.20. You can also get three orders of fries and seven burgers for $38.60. What is the cost of each item?\r<BR>\n" );
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document.write( "1x + 1y = 7.20<BR>\n" );
document.write( "[-1x      -1x]<BR>\n" );
document.write( "y = -1x + 7.20\r<BR>\n" );
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document.write( "3x + 7y = 38.60 <BR>\n" );
document.write( "[-3x         -3x]<BR>\n" );
document.write( "7y = -3x + 38.60<BR>\n" );
document.write( "[/7    /7      /7]<BR>\n" );
document.write( "y = -3/7x + 5.51   \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580548 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=580548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you're on the right track.<BR>\n" );
document.write( "it's one way to solve the problem.<BR>\n" );
document.write( "there are others.<BR>\n" );
document.write( "i'll follow your logic and finish it for you.\r<BR>\n" );
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document.write( "x = cost of fries.<BR>\n" );
document.write( "y = cost of burger.\r<BR>\n" );
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document.write( "1x + 1y = 7.20<BR>\n" );
document.write( "subtract 1x from both sides of the equation to get:<BR>\n" );
document.write( "y = 7.20 - x\r<BR>\n" );
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document.write( "3x + 7y = 38.60<BR>\n" );
document.write( "subtract 3x from both sides of the equation to get:<BR>\n" );
document.write( "7y = 38.60 - 3x<BR>\n" );
document.write( "divide both sides of the equation by 7 to get:<BR>\n" );
document.write( "y = 38.60/7 - 3x/7<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "y = 5.51 - 3x/7 *****\r<BR>\n" );
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document.write( "***** note that you rounded the intermediate results.  this will cause a rounding error in the final result.\r<BR>\n" );
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document.write( "you have two 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( "y = 7.20 - x<BR>\n" );
document.write( "y = 5.51 - 3x/7\r<BR>\n" );
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document.write( "replace y in the second equation with 7.20 - x in the first equation to get:\r<BR>\n" );
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document.write( "7.20 - x = 5.51 - 3x/7\r<BR>\n" );
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document.write( "subtract 5.51 from both sides of the equation and add x to both sides of the equation to get:\r<BR>\n" );
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document.write( "7.20 - 5.51 = x - 3x/7\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "1.69 = 4x/7\r<BR>\n" );
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document.write( "multiply both sides of the equation by (7/4) to get:\r<BR>\n" );
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document.write( "7/4 * 1.69 = 4/7 * x * 7/4 which becomes:\r<BR>\n" );
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document.write( "2.96 = x *****\r<BR>\n" );
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document.write( "***** it's actually equal to 2.9575 which was rounded to 2.96.   once again, rounding the intermediate results can result in a rounding error when you get to the final result.\r<BR>\n" );
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document.write( "that's the cost of the fries.\r<BR>\n" );
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document.write( "since x + 7 = 7.20, the cost of the burger must be 7.20 - 2.96 = 4.24\r<BR>\n" );
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document.write( "that satisfies your first equation.\r<BR>\n" );
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document.write( "your second equation is 3x + 7y = 38.60\r<BR>\n" );
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document.write( "replace x with 2.96 and y with 4.24 to get:\r<BR>\n" );
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document.write( "3 * 2.96 + 7 * 4.24 = 38.60\r<BR>\n" );
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document.write( "solve the equation to get:\r<BR>\n" );
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document.write( "38.56 = 38.60\r<BR>\n" );
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document.write( "since you rounded your intermediate results to 2 decimal places, the answer won't necessarily be right on, but it's close enough to indicate that you did it right.\r<BR>\n" );
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document.write( "another way to solve the equation would have been:\r<BR>\n" );
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document.write( "x + y = 7.20 (first equation)<BR>\n" );
document.write( "3x + 7y = 38.60 (second equation)\r<BR>\n" );
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document.write( "multiply the first equation by -3 to get:\r<BR>\n" );
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document.write( "-3x - 3y = -21.60 (first equation multiplied by -3)<BR>\n" );
document.write( "3x + 7y = 38.60 (second equation)\r<BR>\n" );
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document.write( "add the equations together to get:\r<BR>\n" );
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document.write( "4y = 17\r<BR>\n" );
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document.write( "solve for y to get y = 4.25\r<BR>\n" );
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document.write( "since x + y = 7.20, then x must be equal to 7.20 - 4.25 = 2.95\r<BR>\n" );
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document.write( "x + y is equal to 720.\r<BR>\n" );
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document.write( "3x + 4y is equal to 3*2.95 + 7*4.25 = 38.60\r<BR>\n" );
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document.write( "this method got you the the exact answer because none of the intermediate results were rounded.\r<BR>\n" );
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document.write( "that won't always happen, but it did in this case.\r<BR>\n" );
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document.write( "with the first method, if you didn't round the intermediate results, you would have gotten the same answer as well.\r<BR>\n" );
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document.write( "rounding the intermediate results leads to possible errors in the final result.\r<BR>\n" );
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document.write( "rounding is only recommended when you get to the final results.\r<BR>\n" );
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document.write( "try not to round the intermediate results.\r<BR>\n" );
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document.write( "if you have to, then round to more decimal places than the final result will be rounded to.\r<BR>\n" );
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document.write( "in this case, if you had rounded to 5 decimal places, you would probably have been right on in the final result using either method.\r<BR>\n" );
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