Breaking Down the Info:

Let the number of cards be N. We may denote Merry as E and Michelle as I but it is not necessary. We can create a table to help organize the information. Another hint is that the total amount of cards is always 2N, so we don't have to add or subtract the amount they give each other, it will just be a total of 2N cards regardless.

After Turn X | Merry | Michelle
1 | \(\frac{4}{3}N\) | \(\frac{2}{3}N\)
2 | \(\frac{8}{9}N\) | \(\frac{10}{9}N\)
3 | \(\frac{34}{27}N\) | \(\frac{20}{27}N\).

Then Merry has 14 more cards than Michelle. \(\frac{34}{27}N - \frac{20}{27}N = 14\).

\(N = 27\)

Answer: B
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Algebra? Nah, I think PITA (Plugging In The Answers) sounds tastier!

Let's try B. They both start with 27. Merry gives 9 to Michelle, so Merry has 18 and Michelle has 36. Michelle gives 12 to Merry, so Merry has 30 and Michelle has 24. Merry gives 10 to Michelle, so Merry has 20 and Michelle has 34. Did Merry end up with 14 more than Michelle? Yep. Done.

Answer choice B.


ThatDudeKnowsPITA
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27 is the Answer as such the equations will be after the two continuous change the 20X /27 and 34x/27