I REALLY NEED HELP WITH THIS 6TH GRADE PROBLEM I dont want weird answers. I need the explanation and the correct answer.

tierra had 5 times as many trading cards as patrick. tierra gave 1/4 of her trading to patrick. patrick then gave 1/3 of his trading cards to tierra. if tierra had 96 more trading cards than patrick in the end, how many trading cards did she have in the beginning?

Given: lines a and b are parallel and line c is a transversal. prove: 2 is supplementary to 8 what is the missing reason in the proof? statement reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem