Question 1031155
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Let *[tex \Large x] represent the total number of tiles at the start.  So we are told that *[tex \Large \frac{x}{12}] is the number of tiles in Box A.  This means that *[tex \Large \frac{11x}{12}] tiles remain to be divided between Box B and Box C.  Since one-fourth of the remaining tiles go into Box B, we know two facts:


1.  The number of tiles in Box B is represented by *[tex \Large \left(\frac{1}{4}\right)\left(\frac{11x}{12}\right)]


2.  The number of tiles in Box C is represented by 1 minus the number of tiles in Box B which is to say:  *[tex \Large \left(\frac{3}{4}\right)\left(\frac{11x}{12}\right)]


But we also know that there are 22 more tiles in Box C than in Box B, so another representation of the number of tiles in Box C is *[tex \Large \left(\frac{1}{4}\right)\left(\frac{11x}{12}\right)\ +\ 22]


Since we have two expressions for the same value, we can set them equal to each other:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(\frac{3}{4}\right)\left(\frac{11x}{12}\right)\ =\ \left(\frac{1}{4}\right)\left(\frac{11x}{12}\right)\ +\ 22]


Solve for *[tex \Large x] and then calculate *[tex \Large \frac{x}{12}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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