Ann gave Betty as many cents as Betty had. Betty then gave Ann as many cents as Ann then had. At this point, each had 12 cents. How much did Ann have at the beginning?

Work backward.  If at the end they both had 12 cents.  Then Betty had to have given Ann 6 cents.  Which means that Betty had to have had 18 cents, because there is always a total of 24 cents.  Which meant that before that, Betty had 9 and was given 9 cents.  So Betty originally had 9 cents.  So Ann had 24 minus 9 or 15 cents at the beginning.

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