document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068208>Question 1068208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Building A is 338 meters taller than building B. If the height of building A is subtracted from twice the height of building&#8203; B, the result is 131 meters. How tall is each&#8203; skyscraper?\r<BR>\n" );
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document.write( "During his tennis career in singles&#8203; play, John won 33 fewer tournament A titles than tournament B titles and 22 more tournament C titles than tournament B titles. If he won 20 of these titles&#8203; total, how many times did he win each&#8203; one?<BR>\n" );
document.write( "John won <BR>\n" );
document.write( "nothing tournament A&#8203; title(s).<BR>\n" );
document.write( "John won <BR>\n" );
document.write( "nothing tournament B&#8203; title(s).<BR>\n" );
document.write( "John won <BR>\n" );
document.write( "nothing tournament C&#8203; title(s). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683669 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=683669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first question:\r<BR>\n" );
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document.write( "Building A is 338 meters taller than building B. If the height of building A is subtracted from twice the height of building&#8203; B, the result is 131 meters. How tall is each&#8203; skyscraper? \r<BR>\n" );
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document.write( "let a = the height of building A and b = the height of building B.\r<BR>\n" );
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document.write( "you get a = b + 338\r<BR>\n" );
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document.write( "if you subtract the height of building A from twice the height of building B, then you get:\r<BR>\n" );
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document.write( "2b - a = 131.\r<BR>\n" );
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document.write( "you have 2 equations to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "a = b + 338<BR>\n" );
document.write( "2b - a = 131\r<BR>\n" );
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document.write( "in the second equation, replace a with its equivalent value from the first equation to get:\r<BR>\n" );
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document.write( "2b - (b + 338) = 131\r<BR>\n" );
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document.write( "simplify to get 2b - b - 338 = 131\r<BR>\n" );
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document.write( "combine like terms to get b - 338 = 131\r<BR>\n" );
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document.write( "add 338 to both sides of the equaiton to get b = 469.\r<BR>\n" );
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document.write( "that's the height of building B.\r<BR>\n" );
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document.write( "since building A is 338 meters higher than that, then building A must be 807 meters high.\r<BR>\n" );
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document.write( "you get building A is 807 meters high and building B is 469 meters high.\r<BR>\n" );
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document.write( "building A is 807 - 469 = 338 meters higher than building B.\r<BR>\n" );
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document.write( "if you subtract the height of building A from twice the height of building B, you get 2 * 469 - 807 = 938 - 807 = 131 meters difference.\r<BR>\n" );
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document.write( "solution to the first question looks good.\r<BR>\n" );
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document.write( "building A is 807 meters high and building B is 469 meters high.\r<BR>\n" );
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document.write( "second question:\r<BR>\n" );
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document.write( "During his tennis career in singles&#8203; play, John won 33 fewer tournament A titles than tournament B titles and 22 more tournament C titles than tournament B titles. If he won 20 of these titles&#8203; total, how many times did he win each&#8203; one?\r<BR>\n" );
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document.write( "let a = number of tournament A titles won.<BR>\n" );
document.write( "let b = number of tournament B titles won.<BR>\n" );
document.write( "let c = number of tournament C titles won.\r<BR>\n" );
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document.write( "since total number tournament titles won is 20, you get:\r<BR>\n" );
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document.write( "a + b + c = 20\r<BR>\n" );
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document.write( "since he won 33 fewer tournament A titles than tourament B titles, you get:\r<BR>\n" );
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document.write( "a = b - 33\r<BR>\n" );
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document.write( "since he won 22 more tournament C titles than tournament B titles, you get:\r<BR>\n" );
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document.write( "c = b + 22.\r<BR>\n" );
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document.write( "replacing a and c with their equivalent values from the first 2 equations, you get the third equation becoming:\r<BR>\n" );
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document.write( "b - 33 + b + b + 22 = 20\r<BR>\n" );
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document.write( "combine like terms to get 3b - 11 = 20\r<BR>\n" );
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document.write( "add 11 to both sides to get 3b = 31\r<BR>\n" );
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document.write( "divide both sides by 3 to get b = 10 and 1/3.\r<BR>\n" );
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document.write( "since a = b - 33, this makes a = - (22 and 2/3).\r<BR>\n" );
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document.write( "since c = b + 22, this makes c = 32 and 1/3.\r<BR>\n" );
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document.write( "a + b + c = 20, but .....\r<BR>\n" );
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document.write( "a is negative which can't be, indicating there is something wrong with the equation.\r<BR>\n" );
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document.write( "i suspect that the total number of tournaments won have to be a number greater than or equal to 33 in order for a to be greater than or equal to 0.\r<BR>\n" );
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document.write( "i don't believe there is a valid solution to this problem the way it is presented.\r<BR>\n" );
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document.write( "first of all, the value of b was not an integer.\r<BR>\n" );
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document.write( "second of all, the value of a is negative.\r<BR>\n" );
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document.write( "these are two indications that there is something wrong with the equation the way it is presented.\r<BR>\n" );
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document.write( "i suspect the problem is in the number of tournaments won, but that's just a guess.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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