We could also try answers. Start with answer C, so you know whether to go up (if C is too small) or down (if C is too big).
Let's say x = 24. After the first play she has 11 chips. After the next play she has 4.5 chips. 24 was too small, so we'll move up.
We also learn (from that last example) that x must be even, or we'll get fractional chips on the first play. (There are other conditions too to ensure that x is an integer after both plays, but we don't need to bother sorting them out: we'll just try the next few even numbers up until we find the answer.)
Let's say x = 26. After the first play she has 12 chips. After the next play she has 5 chips. Success! With clever use of the answer choices, we only had to try two numbers, and we're done much faster than we would have been with the algebraic approach I gave earlier.
