<h2>
The number of small buses used = 5</h2><h2>
The number of big buses used = 4</h2>
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
