working with missing values

Question

The state fair is a popular field trip destination. This year the senior class at Oak Hills High School and the senior class at Columbus High School both planned trips there. The senior Class at Oak Hills rented and filled 12 vans and 5 buses with 292 students. Columbus High School rented and filled 6 vans and 12 buses with 450 students. Each van and bus carried the same number of students. What was the number of students in each bus?

Answer 1

12 vans and 5 buses for the first school carrying 292 students

6 vans and 12 buses for the second school carrying 450 students

Let v=number of vans

let b=number of buses

so

12v+5b=292

6v+12b=450

Multiply the second equation by -2 to get

-12v+-24b=-900

12v+5b=292

so -19b=-608

b=32

and then substitute 32 for b

12v+5(32)=192

12v=132

v=11