The senior classes at high school A and High School B planned separate trips to Yellowstone National Park. The senior class at high school A rented and filled 13 vans and 13 buses with 468 students. High school B rented and filled 3 vans and 13 buses with 368 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. Show your work.

Question

Aggie

Biology

3 December, 01:46

The senior classes at high school A and High School B planned separate trips to Yellowstone National Park. The senior class at high school A rented and filled 13 vans and 13 buses with 468 students. High school B rented and filled 3 vans and 13 buses with 368 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. Show your work.

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Answers (1)

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Brian Sexton · Answer 1

Short answer: There are 10 students in each van and 26 students in each bus.

13x+13y=468

3x+13y=368

3x+13y+100=468

3x+13y+100=13x+13y

3x+100=13x

100=10x

100/10=x

10=x

130+13y=468

468-130=13y

338=13y

338/13=y

26=y

So, x=10 and y=26. There are 10 students in each van and 26 students in each bus.

Checking my work:

(13*10) + (13*26) = 130+338=468

(3*10) + (13*26) = 30+338=368