Question 15

Explanation

Defining Variables

Let:

• Number of type $\text{I}$ trucks be $x$.
• Number of type $\text{II}$ trucks be $y$.
• Number of type $\text{III}$ trucks be $z$.

Forming System of Equations

From the problem, we know:

1. The total number of trucks rented is $20$.

   $$x + y + z = 20 \quad \dots (1)$$

2. The total carrying capacity is $96$ kg, with capacities for each type being $3$, $4$, and $6$ kg, respectively.

   $$3x + 4y + 6z = 96 \quad \dots (2)$$

3. It is known that the company rents $4$ type $\text{I}$ trucks.

   $$x = 4$$

Solving the System

Substitute $x = 4$ into equation $(1)$:

Substitute $x = 4$ into equation $(2)$:

Simplify the equation above by dividing both sides by $2$:

Eliminate variable $z$ from equations $(3)$ and $(4)$. Multiply equation $(3)$ by $3$:

Subtract the second equation from the first:

Thus, the number of type $\text{II}$ trucks rented is $6$.