Fatimah had some two-dollar and five-dollar notes in her money box. She had 3 fewer two-dollar notes than five-dollar notes. She then exchanged 4 five-dollar notes for two-dollar notes. How many more two-dollar notes than five-dollar notes did she have in the end?

1. Determine the change in the number of five-dollar notes

Fatimah exchanged $4$ five-dollar notes, so the number of five-dollar notes decreased by $4$.

2. Determine the change in the number of two-dollar notes

The value of $4$ five-dollar notes is $4 \times \char36{}5 = \char36{}20$.
The number of two-dollar notes she received is $\char36{}20 \div \char36{}2 = 10$.
So, the number of two-dollar notes increased by $10$.

3. Calculate the final difference between the number of two-dollar and five-dollar notes

Initially, two-dollar notes were $3$ fewer than five-dollar notes.
Let the initial number of five-dollar notes be $u$.
Initial two-dollar notes = $u - 3$.
Final five-dollar notes = $u - 4$.
Final two-dollar notes = $(u - 3) + 10 = u + 7$.
Difference = Final two-dollar notes - Final five-dollar notes = $(u + 7) - (u - 4) = 7 - (-4) = 11$.