Sophia’s school took a field trip. A total of 21 vechicles were needed for the trip. Some students took the bus, and some studen ts 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?
2 answers:
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...
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.
!! Hope It Helps !!
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