Sophia’s school took a field trip. a total of 21 vechicles were needed for the trip. some students took the bus, and some students car-pooled. there were 30 people on each bus and 4 people in each car. 318 people altogether attended the trip. how many buses and cars were needed for the trip?

Let,
Buses = x
Cars = y

1st Case,
x+y = 21

2nd Case,
30x+4y = 318

Solving both equations,
x+y = 21
30x+4y = 318
__________

Increasing 1st Case equation by 4 times,
Now,

4x+4y = 84
-30x(-)+4y = -318
__________
Subtracting 2nd from 1st,
__________
-26x = -234
x =
[x = 9]

Now, putting value in 1st Case equation,
x+y = 21
9+y = 21
y = 21-9 = 12
[y = 12]

As per our consideration,
x = Buses & y = Cars

[Buses = 9] & [Cars = 12]

So, There are 9 buses and 12 cars.