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

Answer:

Number of students in each van = 18

Number of students in each bus = 53

Step-by-step 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)

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

$778-14y+7y=407\\778-407=7y\\7y=371\\y=\frac{371}{7}=53$

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