Seorang supervisor menerima Rp.60.000 lebih banyak dari 2 kali yang diterima bawahanya per hari. Kalau supervisor bekerja 5 hari dan bawahanya 10 hari mereka menerima Rp.2.100.000. Berapa banyak penghasilan mereka masing-masing?

Let's denote the daily wage of the subordinate as \( S \) (in Rp) and the daily wage of the supervisor as \( R \) (in Rp).

According to the problem, the supervisor receives Rp 60,000 more than twice the subordinate's daily wage. This can be written as:
\[ R = 2S + 60,000 \]

The total earnings for both over their respective working days are:
- The supervisor works 5 days, so their total earnings are \( 5R \).
- The subordinate works 10 days, so their total earnings are \( 10S \).

Together, their total earnings amount to Rp 2,100,000. Thus:
\[ 5R + 10S = 2,100,000 \]

Now we have a system of two equations:
1. \( R = 2S + 60,000 \)
2. \( 5R + 10S = 2,100,000 \)

Let's substitute the first equation into the second equation:

\[ 5(2S + 60,000) + 10S = 2,100,000 \]

Distribute and simplify:

\[ 10S + 300,000 + 10S = 2,100,000 \]

Combine like terms:

\[ 20S + 300,000 = 2,100,000 \]

Subtract 300,000 from both sides:

\[ 20S = 1,800,000 \]

Divide both sides by 20:

\[ S = \frac{1,800,000}{20} \]

\[ S = 90,000 \]

Now, substitute \( S = 90,000 \) back into the first equation to find \( R \):

\[ R = 2(90,000) + 60,000 \]

\[ R = 180,000 + 60,000 \]

\[ R = 240,000 \]

So, the subordinate's daily wage is Rp 90,000 and the supervisor's daily wage is Rp 240,000.

To confirm, we can check the total earnings:

For the subordinate:
\[ 10 \times 90,000 = 900,000 \]

For the supervisor:
\[ 5 \times 240,000 = 1,200,000 \]

Total earnings together:
\[ 900,000 + 1,200,000 = 2,100,000 \]

The calculations are correct. Thus, the subordinate earns Rp 90,000 per day and the supervisor earns Rp 240,000 per day.

Would you like any more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the solution change if the supervisor received Rp 50,000 more than twice the subordinate's wage?
2. What would be the supervisor's daily wage if the subordinate earned Rp 100,000 per day?
3. How can we set up and solve similar problems with different total earnings and working days?
4. What is the impact on the total earnings if both the supervisor and subordinate work additional days?
5. How do you verify solutions to ensure they meet all given conditions in word problems?

**Tip:** When solving word problems, carefully define variables and write down all equations derived from the problem statements to ensure accuracy.

Learn how to solve a system of linear equations involving a supervisor and a subordinate's daily wages. This problem uses algebraic concepts, such as linear equations and substitution method, to determine their respective earnings based on given conditions. Suitable for students in Grades 8-10.

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