Question

Ashley’s school took a field trip. A total of 32 vehicles were needed for the trip. Some students took the bus, and some students car-pooled. There were 27 people on each bus and 3 people in each car. 408 people altogether attended the trip. How many buses and cars were needed for the trip?

Answer 1

19 cars

13 buses

Explanation:

We have a system of equations as follows

X + y = 32 -----1

3x + 27y = 408 ----2

x = car

y = bus

From equation 1

x + y = 32

x = 32 - y ---- 3

We put equation 3 into equation 2

3(32-y) + 27y = 408

96y -3y + 27y = 408

96 + 24y = 408

24y = 408 - 96

24y = 312

Divide through by 24 to get the value of y

Y = 312/24

Y = 13

We put the value of y in equation 3

x = 32 - 13

x = 19

So 19 cars would be needed for the trip and also 13 buses would also be needed