Land Problem
Math brain teasers require computations to solve.
A, B, and C each had land: am^2 (m^2=square meters), bm^2, and cm^2 (this is c square meter, not square centimeter!) big. A sold 1/4 of his land to B, then B sold 1/3 of the land he had (after he bought land from A) to C. If A, B, and C now have the same amount of land, what does (b+c)/a equal to?
HintI advise that you use a letter (ex: k) to compare the three measures.
(and just in case, 1/3 is read as onethird, and so on.)
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Answer
5/4
(multiplication symbols are not written down)
Steps: (3/4)a=2/3((1/4)a+b)=1/3((1/4)a+b)+c
3a/4=(a+4b)/6=(a+4b+12c)/12=k
a=(4/3)k, b=(7/6)k, c=(1/2)k
(b+c)/a = (7k/6 + 1k/2)/(4k/3) = (10k/6)(3/4k) = 5/4
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Comments
pureblue
Aug 16, 2010
 I'm truly confused....
from the start they all have the same amount of land, then A sold 1/4 of his land to B then B sold 1/3 of his total land (after buying from A) to C. So how come they have equal amount of land at the end?
Sorry...
And about the Buy and Sell:
You said that B sell his land to C after buying from A, so you must first add the 1/4 from A before you get the 1/3 from the total land owned by B then sell it to C... As per your answer.
Please clarify... Thanks 
pureblue
Aug 16, 2010
 Sorry, I mistaken at the first part of my comment.... peace 
stil
Aug 16, 2010
 I haven't followed other categories but math certainly seems to be going downhill. Without faulting the author who probably did her best, this is question is below par. First, it is not unlike many others that concern apportionment. Second, it names the variables which makes it even more textbookish than textbooks. (It is possible to ask how the original holdings of B and C together compared to the original holdings of A without declaring the ratio (b+c)/a.) Third, it takes less effort to consistently spell out "square meters" than that invloved in explaining "cm^2". Maybe Koreans do land dealings in square meters; it feels odd that hectares, ares, or acres weren't used. [Or, something really simple like grams of gold or liters of wine.]
Finally, (and this is addressed to the author) the k variable is rather artificial, i.e. unnecessary.
When both land deals are completed,
(3/4)A = (2/3)((A+4B)/4)
3A = (2/3)A + (8/3)B
(7/3)A = (8/3)B
(7/A = B
(2/3)((A+4B)/4) = (1/3)((A+4B)/4) + C
(1/3)((A+4B)/4) = C
A+4B = 12C
A+4(7/A = 12C
(9/2)A = 12C
(9/24)A = C
B+C = [(7/+(9/24)]A = [(21+9)/24]A = (30/24)A = (5/4)A. 
stil
Aug 16, 2010
 @#$& the fickle text editor!
eightrightparenthesis or 8 ) comes through as .
And while we're at it what happens to a stacked 1/2 and some other special characters. ½ π √ ⅞ № 
stil
Aug 16, 2010
 I am calmer now and delighted by possibility that superscripts like ² and ³ might escape mangling by the text editor. 
stil
Aug 16, 2010
 If this test on [suppressed object] 8[U+FFFC]) 8 ) doesn't yield immediately adjacent 8 and ) maybe someone can teach us a backspace or zerowidth character. 
addspras
Aug 19, 2010
 a good teaser, nice and challenging! 
quizwizAhn
Sep 07, 2010
 Why are you saying anything about Koreans Stil?! The only reason I picked square meters instead of acres or stuff is just because I prefer it(For example, I will probably never use the terms pound or ounce for my math teasers). And don't be so harsh on me since this is like my first teaser. By the way, there is also a Korean system for vastness(? I can't find the exact word) of land called 'Pyeong' but it isn't very acurate, so there are campaigns about using the meteric system instead. 
quizwizAhn
Sep 07, 2010
 Oh, and by the way, if you are still not satisfied about why their lands are so small, just think that they are not land dealers, but farmers or something with a little bit of land, OK? 
eddandi
Apr 06, 2011
 as the problem is written the correct answer is 2. the question should be "what does what does (b+c)/a equal at the start." 
quizwizAhn
May 17, 2011
 For those who are confused, (I mean especially you, eddandi), a, b, and c ARE the ORIGINAL areas of lands for A, B, and C.
Therefore, I did NOT have to mention that you have to caculate with the areas that we started with. 
misnilrap
Nov 25, 2015
 I have an easier answer to this.
(b+c+1/4a)/(3/4a)=2
b+c+1/4a=6/4a
b+c=5/4a
(b+c)/a=5/4 
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