Question

7) 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 2 vans
and 7 buses with 407 students. High School B rented and filled 1 van and 7 buses with
389 students. Every van had the same number of students in it as did the buses. How
many students can a van carry? How many students can a bus carry?

Answer 1

Number of students in each van = 18

Number of students in each bus = 53

Explanation:

Given: The senior class at High School A rented and filled 2 vans and 7 buses with 407 students.

High School B rented and filled 1 van and 7 buses with 389 students.

Also, every van and the van had the same number of students in it.

Solution:

Let x denotes number of students in each van and y denotes number of students in each bus.

According to the given information,

`2x+7y=407\,\,\,(i)\\x+7y=389\,\,\, (ii)`

From (ii), put
`x=389-7y` in (i)

`2(389-7y)+7y=407`

`778-14y+7y=407\\778-407=7y\\7y=371\\y=(371)/(7)=53`

Put
`y=53` in
`x=389-7y`

`x=389-7(53)\\=389-371\\=18`

Number of students in each van = 18

Number of students in each bus = 53