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 $w$.

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.