Answer:
Denzel had 90 pretzel sticks before he gave any away.
Explanation:
1) He gives away 2/9 to Jane (He's got 7/9 pretzel sticks left after Jane).
2) The remaining pretzel sticks are broken into 6 portions. He gives away 1/6 to Hannah. Now he's got 5/6 pretzel sticks remaining. We are told that these 5 parts are worth 55 pretzel sticks.
3) 55 pretzel sticks divided into 5 equal parts is 11 pretzel sticks in each.
4) 2/9 + 1/6 pretzel sticks given away needs common denominators to add
4/18 +3/8 = 7/18 pretzel sticks given away in total
That means 11/18 pretzel sticks remained that he did not give away. We are told the 11/18 represents his remaining 55 pretzel sticks.
5) Since we have now divided the whole lot of pretzel sticks into 18 pieces we have 7/18 given away plus 11/18 (55 remain), and we calculated each part is 5 pretzel sticks.
6) 5 x 18 parts = 90 pretzel sticks to begin with.