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The problem you've provided is about calculating the salary of a car sales representative based on a given formula. Let's break it down step by step:

### Given Information:

- The salary of the sales representative is denoted by \( G(x) \), where:
  \[
  G(x) = Rp 1,000,000x + Rp 500,000
  \]
  \( x \) represents the number of cars sold in a given month.

- Additionally, there is a **bonus** if the sales representative surpasses a target. The bonus is **20% of the salary** if the sales exceed the target number of cars.

- You are asked to create a function for the total salary (with the bonus) and calculate how many cars need to be sold if the total salary received is **Rp 5,400,000**, given that the target for car sales per month is **3 cars**.

---

### Step 1: Define Salary without Bonus
The base salary function is given as:
\[
G(x) = 1,000,000x + 500,000
\]
This represents the salary without any bonus.

### Step 2: Add the Bonus Condition
If the sales exceed the target of 3 cars, the sales representative earns a bonus of 20% of the base salary \( G(x) \).

Let the bonus function \( B(x) \) be defined as:
\[
B(x) = 0.2 \times G(x) = 0.2 \times (1,000,000x + 500,000)
\]
Thus, the total salary with the bonus is:
\[
S(x) = G(x) + B(x) = G(x) + 0.2 \times G(x)
\]
Simplifying the expression:
\[
S(x) = 1.2 \times G(x)
\]
But this bonus applies only when \( x > 3 \) (i.e., when the sales exceed the target of 3 cars).

### Step 3: Create the Total Salary Function
The total salary function \( T(x) \) is thus:
\[
T(x) = \begin{cases} 
G(x) & \text{if } x \leq 3 \\
1.2 \times G(x) & \text{if } x > 3
\end{cases}
\]

### Step 4: Calculate the Number of Cars Sold
We are asked to find how many cars need to be sold if the total salary is **Rp 5,400,000**.

First, we'll calculate the base salary for selling exactly 3 cars:
\[
G(3) = 1,000,000(3) + 500,000 = 3,000,000 + 500,000 = Rp 3,500,000
\]
Since \( 5,400,000 > 3,500,000 \), the sales representative must have exceeded the target (i.e., sold more than 3 cars) and received a bonus.

Now, for \( x > 3 \), the total salary with the bonus is:
\[
S(x) = 1.2 \times G(x) = 1.2 \times (1,000,000x + 500,000)
\]
We are given that \( S(x) = Rp 5,400,000 \), so we solve:
\[
1.2 \times (1,000,000x + 500,000) = 5,400,000
\]
Dividing both sides by 1.2:
\[
1,000,000x + 500,000 = \frac{5,400,000}{1.2} = 4,500,000
\]
Solving for \( x \):
\[
1,000,000x = 4,500,000 - 500,000 = 4,000,000
\]
\[
x = \frac{4,000,000}{1,000,000} = 4
\]

### Final Answer:
The sales representative must sell **4 cars** to earn a total salary of **Rp 5,400,000**.

---

Would you like more details on any of the steps? Here are 5 related questions to deepen your understanding:

1. How does the total salary change if the sales representative sells more than 4 cars?
2. What happens if the target is raised to 5 cars instead of 3?
3. How does the function \( T(x) \) behave for large values of \( x \)?
4. How would the solution change if the bonus percentage were different (e.g., 25%)?
5. What would the base salary be for selling 2 cars?

**Tip:** Always break down complex functions into their components (like base salary and bonus) to handle them more easily.

Gaji yang diberikan kepada sales mobil baru pada suatu dealer dinotasikan dengan fungsi G(x) = Rp 1.000.000x + Rp 500.000,00 dengan x banyak unit mobil yang dapat dijual pada bulan itu. Namun, gaji yang dibayarkan ini akan mendapat bonus 20% dari gaji jika target penjualan mobil pada bulan itu dapat sesuai target. Misalkan total gaji yang dibayarkan jika seorang sales mendapat bonus untuk setiap penjualan dengan x gaji pokok dinotasikan dengan B(x). Konstruksi fungsi B(x), kemudian gunakan hasilnya untuk mengonstruksi fungsi komposisi untuk menotasikan total gaji yang diterima sales jika pada bulan itu ia mampu melampaui target penjualan. Misalkan target mobil yang dijual tiap bulannya adalah 3 unit produk. Berapa banyak unit yang diselesaikan jika gaji yang diterima Rp 5.400.000,00?

Learn how to calculate the total salary of a car sales representative based on sales target and bonus. The problem involves calculating salary with a bonus of 20% for exceeding the sales target of 3 cars per month. Suitable for high school students.

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