The cost of the popcorn is $5 x 80/100 = $<<5*80/100=4>>4.
The cost of a can of soda is $4 x 50/100 = $<<4*50/100=2>>2.
The cost of 4 tickets is $5 x 4 = $<<5*4=20>>20.
The cost of 2 sets of popcorn is $4 x 2 = $<<4*2=8>>8.
The cost of 4 cans of soda is $2 x 4 = $<<2*4=8>>8.
Therefore, the family paid a total of $20 + $8 + $8 = $<<20+8+8=36>>36.
#### 36