To increase the amount by £5, Alison can:
- Cancel 2 deposit and cancel 3 withdrawals: 2 x (-£2) + 3 x (£3)
- Do 4 deposits and do 1 withdrawal: 4 x (£2) + 1 x (-£3)
The 2 of the above sets of transactions can result in a net increase of £5 to the account. In addition, adding any transactions sets including 3 deposits and 2 withdrawals or cancelling 3 deposits and cancelling 2 withdrawals, and the multiple of these will not affect the balance. Therefore, there are infinite ways.
For other ways to change, Alison can increase the account balance by £1 by either:
- Do 2 deposit and do 1 withdrawal: 2 x (£2) + 1 x (-£3)
- Cancel 4 deposits and cancel 3 withdrawals: 4 x (-£2) + 3 x (£3)
Any multiples of the above sets of transactions can result in a net increase of £1 to the account.
For other ways to change, Alison can decrease the account balance by £1 by either:
- Cancel 2 deposit and cancel 1 withdrawal: 2 x (-£2) + 1 x (£3)
- Do 4 deposits and do 3 withdrawals: 4 x (£2) + 3 x (-£3)
Any multiples of the above sets of transactions can result in a net decrease of £1 to the account.
To conclude, there are infinite ways to change the balance by any amounts as long as the transactions are in the multiple of the sets above.