SOLUTION: A youth group with 26 members is going skiing. Each of the five chaperons will drive a van or a sedan. The vans can seat seven people, and the sedans can seat five people. How many

Question 161323: A youth group with 26 members is going skiing. Each of the five chaperons will drive a van or a sedan. The vans can seat seven people, and the sedans can seat five people. How many of each type of vehicle could transport all 31 people to the ski area in one trip?
I really need help I do not understand this word problem at all please help me
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
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' ;)

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