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We let the original number of cookies be x

Her friend received (3/5)x while her brother received (3/4)(2/5)(x) or (3/10)x

The difference between the friend's number of cookies to the brother is 15 so:
(3/5)x - (3/10)x = 15
(3/10)x = 15
x = 15(10/3) = 50

Final answer:
Mrs. Chan baked 50 cookies at first with the friend receiving 30 cookies and the brother receiving 15 cookies.