Answer: 2 buses and 4 vans would be needed
Step-by-step explanation:
Let x represent the number of buses that would be needed.
Let y represent the number of vans that would be needed.
There will be six drivers, and two different types of vehicles. This means that
x + y = 6
142 students are going on a field trip. A bus can hold 51 people while a van can hold 10. This means that
51x + 10y = 142 - - - - - - - - - - - 1
Substituting x = 6 - y into equation 1, it becomes
51(6 - y) + 10y = 142
306 - 51y + 10y = 142
- 51y + 10y = 142 - 306
- 41y = - 164
y = - 164/ - 41
y = 4
x = 6 - y = 6 - 4
x = 2
