To find the total cost of Alex and Leandro's purchases, we need to consider the cost of the movie tickets, drinks, and bags of popcorn.
- The cost of the two movie tickets is \(6.50 \times 2 = 13.00\).
- Let \(d\) represent the number of drinks purchased, with each costing \(5.50\).
- Let \(p\) represent the number of bags of popcorn purchased, each costing \(6.00\).
So, the correct expression representing the total cost would be:
\[ 13 + 5.50d + 6p \]
Thus, the first option, 13 + 5.50d + 6p, is the correct expression.