Question

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?

Answer 1

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