Question

The state fair is a popular field trip destination. This year the senior class at High School A and

the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 3 vans and 12 buses with 693 students. High School B rented and filled 2 vans
and 2 buses with 138 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

1 bus = 15 students, 1 van = 54 students

Explanation:

A: 3v + 12b = 693

B: 2v + 2b = 138

Add 555 to both sides of equation B to make the sums equal.

2v + 2b + 555 = 693

This can also be seen as:

2v + 2b + 555 = 3v + 12b

Subtract 2v from both sides.

2b + 555 = v + 12b

Subtract 2b from both sides.

555 = v + 10b

With some guess and check, and substituting:

1 bus = 15 students, 1 van = 54 students