The local amusement park 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 12 vans and 1 bus with 211 students. High school b filled 11vans and 9 buses with 541 students. Every van had the same number of student in it as did the buses. How many students can a van carry? How many students can a bus carry?

Bus carries 58 students

Van carries 18 students

Let v be the number of students a van can carry

Let b be the number of students a bus can carry

Equations:

16v + 8b = 752

5v + 5b = 380; b = (380-5v) / 5

Substitute b to the first equation:

16v + 8 (380-5v) / 5 = 752

8 (380-5v) / 5 = 752 - 16v

(3040 - 40v) / 5 = 752 - 16v

3040 - 40v = (752 - 16v) 5

3040 - 40v = 3760 - 80v

-40v + 80v = 3760 - 3040

40v = 720

v = 18

b = (380-5v) / 5 = (380-5{18}) / 5 = (380 - 90) / 5

b = 290/5 = 58