SOLUTION 2: Dinner

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We'll start where it says How to Solve.
First make a table of what you know:

• 4 appetizers, 3 are REGULAR and take 5 minutes to finish and 1 has bread which takes 7 minutes to finish. A regular appetizer takes 5 minutes to finish but with bread it takes 2 MORE minutes to finish.

• 6 beverages, 4 are REGULAR and take 5 minutes to finish and 2 are smoothie like which takes 6 minutes to finish.

• 10 main course, 4 are REGULAR and take 25 minutes to finish and 6 have steak which takes 30 minutes to finish.

• 5 desserts, 2 are REGULAR and take 5 minutes to finish and 3 are brownie like which takes 7 minutes to finish.

Since Sebastian wants to have an appetizer, beverage, main course, dessert and finish in 45 minutes or less there's really only two cases. There are only two cases because:

• He can have everything that requires more time to eat or "extra" time except for the main course because that would elapse his time that he wanted to finish. It only takes him 40 minutes to complete dinner if everything was "regular" and since it takes a total of 5 minutes to finish an "extra" appetizer + "extra" beverage + "extra" dessert that works out perfectly to 45 minutes.

• He can also have everything remain regular and only change his main course because if he decides to have an "extra" as a main course it would take another 5 minutes to complete his dinner which works out to 45 minutes.

CASE 1

In the first case we would have four slots for four different dishes because each of those dishes have a number of choices to be chosen. There are 4 different dishes to choose for appetizers because he could either choose a regular appetizer or one that requires more time to finish. The second slot would be 6 because he could either choose a regular beverage or one that requires more time to finish. The third slot would be 4 because it HAS to be a regular dish. The reason why it has to be a regular dish is because if he choose the first one to be an extra and the second to be an extra he cannot have a main dish that requires more time or he'll go over 45 minutes. The fourth slot has to be 5 because he can either choose a regular or extra.

That number also includes if he chooses everything to be regular and if he would just have two things such as an appetizer and dessert to be the only ones that require a bit more time to eat.


CASE 2

In the second case the only thing that can be "extra" or can be changed is the main course because if it was regular it only takes 25 minutes and if the main course has steak it takes 5 minutes more to finish which then would work out to 45 minutes. So what we would have is all regular items and the main course would change.

He would only have 3 choices for an appetizer because they are regular and don't require any more time to finish. 4 choices for a beverage. For the main course 6 choices because they all have steak in them which would take 5 minutes more to complete. It's not 10 because in the previous case we already have main courses without steak with the rest being regular, so by making the main course 10 different choices, we would have dinners that were the same. 2 choices for dessert because there are 2 regular desserts.

To find the total number of dinner choices Sebastian can have we just simply add cases 1 and 2 and there's your answer.