Well, we know that the total amount is $420, so we can already set one side of the equation. =420. Also, it said that the $420 is (equal to) 7/6b (b for balance). Now just put it together! 7/6b=420 is your answer.
It would still be a 1/6th chance that you will gey the number three. i would say that just because you got 3 5 times in a row will not increase or decrease your chances of another 3.