document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1007090>Question 1007090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Translate the following situation into an equation. Do not solve.\r<BR>\n" );
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document.write( "“Sarah is three times as old as Sam and Mark is eight years younger than Sam. If their average age is 44, how old is Sarah?” </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623098 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=623098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = sarah's age.<BR>\n" );
document.write( "y = sam's age.<BR>\n" );
document.write( "z = mark's age.\r<BR>\n" );
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document.write( "“Sarah is three times as old as Sam and Mark is eight years younger than Sam. If their average age is 44, how old is Sarah?” \r<BR>\n" );
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document.write( "x = 3y (sarah is three times as old as sam).<BR>\n" );
document.write( "z = y - 8 (mark is 8 years younger than sam).<BR>\n" );
document.write( "(x + y + z)/3 = 44 (their average age is 44).<BR>\n" );
document.write( "how old is sarah?\r<BR>\n" );
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document.write( "make sure that when you get a solution that you confirm it to be true by checking it against the original requirements.\r<BR>\n" );
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document.write( "if you run into great difficuty finding a solution, let me know and i'll show you how i did it.\r<BR>\n" );
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document.write( "fyi, you can set up 3 variables and then work on figuring out equivalencies.\r<BR>\n" );
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document.write( "another way is to work with one variable directly, such as the following:\r<BR>\n" );
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document.write( "“Sarah is three times as old as Sam and Mark is eight years younger than Sam. If their average age is 44, how old is Sarah?” \r<BR>\n" );
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document.write( "x = sam's age.<BR>\n" );
document.write( "3x = sarah's age.<BR>\n" );
document.write( "x - 8 = mark's age.\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "x = sarah's age.<BR>\n" );
document.write( "x/3 = sam's age.<BR>\n" );
document.write( "x/3 - 8 = mark's age.\r<BR>\n" );
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document.write( "or:\r<BR>\n" );
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document.write( "x = mark's age.<BR>\n" );
document.write( "x + 8 = sam's age.<BR>\n" );
document.write( "3(x+8) = sarah's age.\r<BR>\n" );
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document.write( "if the average of their ages is 44, then the total of their ages will be 44 * 3 = 132.\r<BR>\n" );
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document.write( "in the first method you would get x + y + z = 132.\r<BR>\n" );
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document.write( "in the second and third and fourth methods, you will get:\r<BR>\n" );
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document.write( "x + 3x + x - 8 = 132 (second method)\r<BR>\n" );
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document.write( "x + (x/3) + (x/3) - 8 = 132 (third method)\r<BR>\n" );
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document.write( "x + x + 8 + 3 * (x + 8) = 132 (fourth method).\r<BR>\n" );
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document.write( "all 4 methods will give you the same answer.<BR>\n" );
document.write( "just be careful as to whose age x represents.\r<BR>\n" );
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document.write( "sometimes i solve them directly as in the second through fourth method.<BR>\n" );
document.write( "sometimes i solve them indirectly as in the first method.\r<BR>\n" );
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document.write( "it depends on the problem and how complex the equations become.\r<BR>\n" );
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document.write( "the first method has advantages in clarity of presentation even though it involves more variables to start wtih.\r<BR>\n" );
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document.write( "the trick is to reduce the number of variables to a number that can be solved either directly or indirectly.\r<BR>\n" );
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document.write( "the general rule for solving directly is that the number of unknown variables and the number of equations should be the same.\r<BR>\n" );
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document.write( "translating the word problem to equations is a most important part of solving these types of problems.\r<BR>\n" );
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document.write( "with practice it gets easier.\r<BR>\n" );
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document.write( "assigning a variable to an unknown quantity is the first part.\r<BR>\n" );
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document.write( "fyi, the solution that i got was:<BR>\n" );
document.write( "sarah = 84<BR>\n" );
document.write( "sam = 28<BR>\n" );
document.write( "mark = 20\r<BR>\n" );
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document.write( " </SPAN>\n" );
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