Question 14

Explanation

Defining Variables

Let:

• Salary of Group $A$ be $x$.
• Salary of Group $B$ be $y$.
• Salary of Group $C$ be $z$.

Forming Equations

From the problem, we know:

1. Salary of Group $A$ is one-third of Group $B$'s salary.

   $$x = \frac{1}{3}y \quad \dots (1)$$

2. Salary of Group $C$ is half of Group $B$'s salary.

   $$z = \frac{1}{2}y \quad \dots (2)$$

Solving the Problem

Asked: Income of Group $A$ for $6$ months is equal to income of Group $C$ for $n$ months.

The equation is:

Substitute equations $(1)$ and $(2)$ into the equation above (express everything in terms of $y$):

Since $y \neq 0$, we can divide both sides by $y$:

Thus, the income will be equal to the income of Group $C$ employees for $4$ months.