Aschool is planning a field trip for 142 people. the trip will use six drivers and two types of vehicles: buses and vans. a bus can seat 51 passengers. a van can seat 10 passengers. write and solve a system of equations to find how many buses and vans will be needed

Six vehicles, buses and vans:
b + v = 6
b = 6 - v

Question: Are the drivers included in the 142 total
persons?

51b + 10v = 142
51(6-v) + 10v = 142
316 - 51v + 10v = 142
-41v = 142-316
-41v = -174
v = 4.2439
b = 1.7561

2 buses and 4 vans: 2(52)+4(11) = 148 person
capacity: 142 attendees and 6 drivers.

Note: each bus holds 52 persons ...
51 passengers and the driver.
Each van holds 11 persons by same logic.. 10+driver

2(10 - 13x) + 9x = -34x + 6020 - 26x + 9x = -34x + distributive property-17x = -34x + subtraction property (subtracted 20 from both sides)17x = addition property (added 34x to both sides)x = 40/ division property (divided both sides by 17)