Sarah drives to work every day, covering a distance of 50 miles each way. She drives at an average speed of 60 miles per hour. Her car consumes fuel at a rate of 25 miles per gallon, and the cost of fuel is $3 per gallon. If Sarah works 22 days a month, what is her monthly fuel expense for commuting? Let's think step by step and output the final answer within \boxed{}.
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