We use units, since ratio does not equal to the exact number of bookmarks they have. 1 unit represents an unknown number of bookmarks (represented as U). After both girls gave away 24 bookmarks each, we have a new ratio, 1:4, which means we require a new unit, for example, X. Note that 1X number of bookmarks is not the same as 1U number of bookmarks. We then form equations linking the initial number to the final number, after giving away 24 bookmarks. Now, we realise that if we multiply (1U-24=1X) by 4, the right hand side of both equations will be 4X. This means that the left hand side of both equations will also be the same. We will get 4U-96=3U-24. Also realise that X units are now gone, so we can simply find the value of U now.

Key:
difference of Before and After is UNCHANGE