If the powers that be don't allowe you the three days but another person 3 weeks,there's clearly something fishy going on.
I'd go. As GT6 pointed out,the non refundable costs allready made is a valid point and if you call in sick,your school could indeed not believe it,but as long as they can't prove you weren't sick or went to Le Mans,you shouldn't have any problems...
Good luck.
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