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The image shows a word problem with three different price combinations involving fruits: salak, jambu, and kelengkeng. The problem asks to find the price of 1 kg of jambu.

Here’s the system of equations from the given dataThe image shows a word problem with three different price combinations involving fruits: salak, jambu, and kelengkeng. The problem asks to find the price of 1 kg of jambu.

Here’s the system of equations from the given 

1. \( 4S + 1J + 2K = 54,000 \)  (Equation 1)
2. \( 1S + 2J + 2K = 43,000 \)  (Equation 2)
3. \( 3S + 1J + 1K = 37,750 \)  (Equation 3)

Where:
- \( S \) is the price of 1 kg of salak,
- \( J \) is the price of 1 kg of jambu,
- \( K \) is the price of 1 kg of kelengkeng.

### Step-by-step solution:

We can solve this system of equations using substitution or elimination. I will calculate this and provide the result.The prices of the fruits are as follows:
- 1 kg of salak (S) = Rp6,500
- 1 kg of jambu (J) = Rp8,500
- 1 kg of kelengkeng (K) = Rp9,750

Therefore, the price of 1 kg of jambu is **Rp8,500**.

Would you like more details on the steps, or do you have any further questions?

Here are five related questions you might want to explore:
1. How would the system change if the price of kelengkeng were reduced by 10%?
2. What would be the price of 3 kg of jambu and 2 kg of salak?
3. Can the system be solved using matrix methods, such as Gaussian elimination?
4. How can you verify the correctness of the result by substituting back into the original equations?
5. How would the total price change if the quantities of fruits were doubled?

**Tip**: When solving systems of equations, substitution or elimination methods work well, but matrix techniques can be quicker for larger systems.

Diketahui harga 4 kg salak, 1 kg jambu, dan 2 kg kelengkeng adalah Rp54.000,00. Harga 1 kg salak, 2 kg jambu, dan 2 kg kelengkeng adalah Rp43.000,00. Harga 3 kg salak, 1 kg jambu, dan 1 kg kelengkeng adalah Rp37.750,00. Harga 1 kg jambu adalah ....

Learn how to solve a system of equations to find the price of 1 kg of jambu. The problem involves three different price combinations of fruits (salak, jambu, and kelengkeng) with a step-by-step solution using algebraic methods. Suitable for students in Grades 9-12.

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