Question

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?

Answer 1

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

Hope it helps...

Answer 2

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 = $\frac{ - 234}{ - 26}$
[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.

!! Hope It Helps !!