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Strange Bank Account (part 2)
Age
11 to 14
Challenge Level
Problem
Getting Started
Student Solutions
Teachers' Resources
This problem follows on from
Strange Bank Account
.
In Charlie's Bank you are only allowed to deposit £2 at a time and withdraw £3 at a time. You can also
cancel transactions
.
Alison found a way of increasing her account balance by £5:
Seven deposits and three withdrawals:
(+ £2) + (+ £2) + (+ £2) + (+ £2) + (+ £2) + (+ £2) + (+ £2) + (- £3) + (- £3) + (- £3)
which Alison wrote as $7\times (+ £2) + 3 \times (- £3)$
She then found another way:
One deposit and
cancelling
one withdrawal, which Alison wrote as $(+ £2) - (- £3)$
Are there other ways in which Alison can
increase the amount of money in her account by £5?
How many ways?
Can Alison change the balance in her account by other amounts in many different ways?
With thanks to
Don Steward
, whose ideas formed the basis of this problem.