### Brain Teasers

# Land Problem

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?

### Hint

I advise that you use a letter (ex: k) to compare the three measures.(and just in case, 1/3 is read as one-third, and so on.)

### 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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