https://file.aiquickdraw.com/mathbot/file/17288751283797w6kdjfx.jpg

Let's analyze the problem set presented in the image.

### Problem 1: Price of Fruits
You are given two equations related to the prices of fruits:
- 1 apple + 1 pineapple costs Rp 10,000
- 2 apples + 1 pineapple costs Rp 13,000

We need to determine the individual prices of the apple and the pineapple by solving this system of equations.

Let:
- \( x \) = price of an apple
- \( y \) = price of a pineapple

From the information:
1. \( x + y = 10,000 \)
2. \( 2x + y = 13,000 \)

We can solve these two equations simultaneously to find the values of \( x \) and \( y \).

### Problem 2: Heights of Objects
We are asked to determine the heights of the plant and the table, where two configurations of the table and plant heights are provided:
- The total height of a table with a plant is 160 cm.
- The height of a table alone is 40 cm.

Let:
- \( z \) = height of the plant
- \( w \) = height of the table

From the information:
1. \( z + w = 160 \)
2. \( w = 40 \)

We can substitute the value of \( w \) to find \( z \).

### Problem 3: Coin Values
There are two types of coins available in a game:
- With Rp 70,000, you can either get:
  - 20 coins of type I and 30 coins of type II, or
  - 25 coins of type I and 20 coins of type II.

Let:
- \( a \) = value of one coin of type I
- \( b \) = value of one coin of type II

From the information:
1. \( 20a + 30b = 70,000 \)
2. \( 25a + 20b = 70,000 \)

We can solve this system of equations to find the values of \( a \) and \( b \).

### Problem 4: Juice Mixture
Initially, there is 300 mL of juice, which is a mixture of orange juice and water. If 20% more orange juice and 50% more water are added, the total becomes 420 mL. We are asked to find the initial amounts of orange juice and water.

Let:
- \( o \) = initial volume of orange juice
- \( w \) = initial volume of water

From the information:
1. \( o + w = 300 \)
2. \( 1.2o + 1.5w = 420 \)

We can solve this system to find \( o \) and \( w \).

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Would you like me to solve all the systems of equations in detail? Here are 5 follow-up questions to explore:

1. How do you solve a system of linear equations using substitution?
2. What is the significance of adding percentages to mixtures in real-life situations?
3. What method would you use for solving larger systems of equations?
4. Can you think of a situation where knowing the height of objects like in Problem 2 could be practically useful?
5. How can unit prices of items be efficiently calculated in business settings?

**Tip:** When working with systems of equations, it’s helpful to start by simplifying one equation to substitute into the other, especially when one variable is already isolated.

Determine the unknown values in the system of linear equations for the price of fruits, heights of objects, coin values, and juice mixture volumes.

Learn how to solve systems of linear equations to find the individual prices of fruits, heights of objects, coin values, and juice mixture volumes. This detailed step-by-step solution is designed for students in Grades 9-11.

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