The Case of Confused Cashier

Taken from South East Asian Mathematics Competition (SEAMC) 2010 in Bangkok, Thailand.

Mr. Smith went into his local bank with a cheque for an amount in Dollars and Cents. He asked the cashier to give him cash for the amount on the cheque. However, she confused the Dollars and cents. So Mr. Smith received Dollars for the amount of cents on the cheque, and cents for the amount of Dollars (e.g if the cheque was for $22.43, Mr. Smith would have been given $43.22)
Mr. Smith left the bank and bought a newspaper for 50 cents. After this, Mr. Smith realised he had exactly three times as much money left as the value of the original cheque.
How much was the original cheque for?

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