Emma’s final sticker count is three times of the original count.

But Emma’s final sticker count is also four times of the original count.

So, we need a good choice of units which can be divided by both 3 and 4.

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We let Emma’s final sticker count be 12 units. Then, Francis’ final sticker count is 3 units, since Emma ends up having four times as many stickers as Francis.

Emma final: 12 units
Francis final: 3 units

Emma actually has three times as many stickers in the end as compared to the start. So in fact, Emma only has 4 units of stickers at the start (and buys 8 more units).

Francis also starts out with 4 units of stickers.

Francis start: 4 units
Francis final: 3 units
Difference: 1 unit

Francis actually loses 8 stickers, so 1 unit represents 8 stickers.

1 unit = 8 stickers
4 units = 32 stickers

Meaning to say, Francis has 32 stickers at first.

I will read through your answer. I did the equation way n manage to get the answer. Tqvm