Maximize Snack and Drink Purchase

Two friends, Mia and Liam, are planning a movie night. Mia has a budget of $60 and plans to buy snacks and drinks. The total cost of snacks is represented by the equation:

$$2x + 3y = 60$$

where $x$ is the number of snack packs costing $2 each, and $y$ is the number of drink cups costing $3 each.

Liam also wants to contribute to the movie night and has a different budget. He plans to buy the same items and has the equation:

$$4x + 2y = 72$$

What is the total number of snack packs $S$ and drink cups $D$ they can buy together if they aim to maximize their purchase while adhering to their budgets? Provide your answer as the sum of $S$ and $D$.