math word problem

Question

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 11 buses with 647 students. High School B rented and filled 14 vans and 1 bus with 187 students. Each van and bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Answer 1

Let x = the number of student that a van can carry and y = the number that a bus can carry.

• High School A rented and filled 13 vans and 11 buses with 647 students:

13x + 11y = 647

• High School B rented and filled 14 vans and 1 bus with 187 students:

14x + y = 187; so y = 187-14x

 

Substitute 187-14x in place of y in the first equation:

 

13x + 11y = 647

13x + 11(187-14x) = 647

13x + 2057 - 154x = 647

-141x =  -1410

 

Solve for x.  Once you have x, y = 187-14x.