A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each and 8 buses of 40 seats, but only has 9 drivers available. The rental cost for a large bus is $800 and $600 for the small bus. Calculate how many buses of each type should be used for the trip for the least possible cost. Let x = the small buses and y = the big buses.

The number of small buses used = 5The number of big buses used = 4

Step-by-step explanation:

Let us assume the total number of small buses needed = x

The capacity of 1 small bus = 40

So, the capacity of x buses = 40 (x) = 40 x

Let us assume the total number of big buses needed = y

The capacity of 1 big bus = 50

So, the capacity of y buses = 50 (y) = 50 y

Also, the total students travelling = 400

So, the number of students traveling by (Small bus + Big bus) = 400

⇒ 40 x + 50 y = 400 ... (1)

Also, the total number of drivers available = 9

⇒ x + y = 9 ... (2)

Also, x ≤ 8, y ≤ 10

Now, solving both equations, we get:

40 x + 50 y = 400 ... (1)

x + y = 9 ⇒ y = (9-x) put in (1)

40 x + 50 y = 400 ⇒ 40 x + 50 (9-x) = 400

or, 40 x + 450 - 50 x = 400

or, - 10 x = - 50

or, x = 5 ⇒ y = (9-x) = 9 - 5 = 4

Hence the number of small buses used = 5

The number of big buses used = 4