Final answer:
Maria will need to order 3 pans of pasta and 5 trays of sandwiches to accommodate 60 guests within her $275 food budget for the graduation party.
Step-by-step explanation:
Maria is preparing for a graduation party and needs to order food within her budget. She plans to invite 60 people and has budgeted $275 for the food. The caterer offers pans of pasta that serve 10 people for $55 each and trays of sandwiches that serve 6 people for $22 each. To determine how many pasta pans and sandwich trays Maria will need to order, let's perform some calculations.
The total number of people is 60. To ensure that there is enough food for everyone, Maria could opt for purchasing 6 pans of pasta (serving a total of 60 people) which would cost her 6 x $55 = $330. However, this exceeds her budget. Instead, Maria can mix and match the two options to stay within her budget.
Let's assume Maria decides to order x pans of pasta and y trays of sandwiches. The equations representing her constraints are:
- 10x + 6y ≥ 60 (to serve at least 60 people)
- 55x + 22y ≤ 275 (to stay within the budget)
Now, Maria needs to find a combination of x and y that satisfies both equations. One possible combination is ordering 3 pans of pasta (3 x $55 = $165) and 5 trays of sandwiches (5 x $22 = $110), yielding a total cost of $165 + $110 = $275, which exactly matches her budget and provides food for exactly 60 people (30 people with pasta and 30 with sandwiches).
Therefore, Maria will need to order 3 pans of pasta and 5 trays of sandwiches to feed 60 people within a budget of $275.