Question 161323
This is a problem that 'sort of' models a real life situation. There are many answers that work, and several that won't.

You have 26 youth and 5 chaperons. That is a total of 31 people.
You can use vans and sedans. Without any info on what the cost associated with each vehicle is, you can't ,make any desicion base don that. What you can do is figure out the combinations of sedans and vans that will work.

Each van can seat 7 people. With 5 chaperons each driving a van, you can take 35 people total. So that works. One answer is 5 vans. That would leave 4 empty seats.

Since each sedan can hold five people, every time you swap a sedan for a van, you lose the ability to take 2 people. So you can use 4 vans and 1 sedan. That combo allows you to take (4*7) + (1*5) = 33. You still have 2 empty seats.

You can use 3 vans and 2 sedans. (3*7) + (2+5) = 31. No more empty seats.

You cannot use more than 2 sedans or you'll need more than one trip.

So you have 3 possible options. In a real life setup, you would probably have some information on how expensive it is to use a van and a sedan (price of gas, maybe rental cost, etc). You would then use the one that make best 'cents' ;)