Question

Sophia's School took a field trip. A total of 21 vehicles 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.Write the system and find how many buses and cars were used.

Answer 1

Letno.of buses be x and no.of cars be y.

30x + 4y = 318......1

x + y = 21

4x + 4y = 84.......2

1-2

30x-4x+4y-4y = 402
26x = 402
X = 15

So, no.of buses are 15

Answer 2

Let the number of buses be x
and car be y

• Total vehicle gone are 21

x + y = 21 ..... ( i ) × 4

• There are 30 people in buses and 4 on car total people gone are 318

30x + 4y = 318 ..... ( ii )

Sub ( ii ) from ( i ) × 4

4x + 4y - ( 30x + 4y ) = 84 - 318

4x + 4y - 30x - 4y = - 234

- 26y = - 234

y = 9

Putting the value of y in eq i

x + y = 21

x = 21 - 9

x = 12

Total buses are 12
and total car are 9