The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 6363 students, requires 88 chaperones, and costs $ 1,200 to rent. Each van can transport 77 students, requires 1 chaperone, and costs $80 to rent. Since there are 567 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 567 students. Since only 80 parents have volunteered to serve as chaperones, the officers must plan to use at most 80 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?

Question

Kaiya Rodriguez

Mathematics

25 July, 00:25

The officers of a high school senior class are planning to rent buses and vans for a class trip. Each bus can transport 6363 students, requires 88 chaperones, and costs $ 1,200 to rent. Each van can transport 77 students, requires 1 chaperone, and costs $80 to rent. Since there are 567 students in the senior class that may be eligible to go on the trip, the officers must plan to accommodate at least 567 students. Since only 80 parents have volunteered to serve as chaperones, the officers must plan to use at most 80 chaperones. How many vehicles of each type should the officers rent in order to minimize the transportation costs? What are the minimal transportation costs?

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Answers (1)

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Mackenzie Huerta · Answer 1

Rent 8 vans, total cost 640 dollars

Step-by-step explanation:

Since a van can accomodate 77 students and 1 chaperone.

To accomodate 567 students vans needed are

567/77 = 7.3

Rounding it off to 8 vans

If the officer places 71 student and 8 chaperones in a van. He can accomodate 65 chaperones and 567 students.

71x8 = 568

But we have only 567 students so in 1 van there will be 70 students and 9 chaperons.

For chaperons

(7x8) + (1x9) = 65

Total cost for transportation will be

8 x 80 = 640 dollars