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February 2nd, 2012, 01:05 PM  #1  
Senior Member Joined: Jan 2010 Posts: 205 Thanks: 0  [SOLVED] Algebra linear equation word problem Quote:
x  y = 13 And now I don't know which one is the bigger or smaller one, so I have to choose from these 2 equations: 2x + 3y = 129 OR 2y + 3x = 129 Since in x  y = 13, it could be something like: 14  1 = 13, or 1  14, or something else. Either number can be smaller or larger. Is there any way I can tell from the getgo which equation I have to use instead of trialanderroring both? Anyway, here is path 1: x  y = 13 2x + 3y = 129 Move over y in the 1st equation: x = y + 13 Plug in the second equation: 2(y + 13) + 3y = 129 2y + 26 + 3y = 129 5y = 103 y = 20.6 x = 20.6 + 13 x = 33.6 This is obviously wrong as the word problem said "twice the smaller" which means "2x" would have made 'x' the smaller number, but 'x' is larger than 'y' for this equation. Path 2: x  y = 13 2y + 3x = 129 x = y + 13 2y + 3(y + 13) = 129 2y + 3y + 39 = 129 5y = 90 y = 18 x = 18 + 13 x = 31 So now this makes sense, because 'y' was the smaller number in this case which is true. Is there any way to avoid the unnecessary work in the future with more variables which would mean more guessing and checking?  
February 2nd, 2012, 01:11 PM  #2  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Algebra linear equation word problem Quote:
 
February 2nd, 2012, 01:14 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond  Re: Algebra linear equation word problem
Pick a variable as the smaller number and make your equations accordingly. Let x be the larger number and y be the smaller number. x  y = 13 (1) 3x + 2y = 129 (2) Multiply (1) by 2: 2x  2y = 26, add this to (2): 5x = 155, x = 31, x  13 = y, y = 18 
February 2nd, 2012, 04:10 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,019 Thanks: 2254 
If the smaller is s, 2s + 3(s + 13) = 129, i.e. 5s + 39 = 129, so s = (129  39)/5 = 18 and s + 13 = 31.


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