https://file.aiquickdraw.com/mathbot/file/1728875227000vr55pigm.jpg

Let's break down and solve each problem from the image.

### Problem 1:
We need to determine the unit price of the fruit:
- **Equation 1:** One pineapple and two apples cost Rp10.000.
- **Equation 2:** One pineapple and three apples cost Rp13.000.

Let:
- \( p \) be the price of one pineapple.
- \( a \) be the price of one apple.

From the given information:
1. \( p + 2a = 10.000 \)
2. \( p + 3a = 13.000 \)

Subtract equation 1 from equation 2:
\[
(p + 3a) - (p + 2a) = 13.000 - 10.000
\]
\[
a = 3.000
\]

Substitute \( a = 3.000 \) into equation 1:
\[
p + 2(3.000) = 10.000
\]
\[
p + 6.000 = 10.000
\]
\[
p = 4.000
\]

So, the price of one pineapple is **Rp4.000**, and the price of one apple is **Rp3.000**.

---

### Problem 2:
We need to determine the heights of the plant and the table.
- **Given:**
  - The total height of the plant and table is 160 cm.
  - The height of the table alone is 40 cm.

Let:
- \( t \) be the height of the table (which is already given as 40 cm),
- \( p \) be the height of the plant.

From the given information:
\[
p + t = 160
\]
Substitute \( t = 40 \):
\[
p + 40 = 160
\]
\[
p = 120
\]

So, the height of the plant is **120 cm**, and the height of the table is **40 cm**.

---

### Problem 3:
We need to determine the price per coin of type I and type II.

Let:
- \( x \) be the price of one coin I,
- \( y \) be the price of one coin II.

- If someone pays Rp70.000, they can get:
  - 20 coins of type I and 30 coins of type II,
  - or 25 coins of type I and 20 coins of type II.

From this, we have two equations:
1. \( 20x + 30y = 70.000 \)
2. \( 25x + 20y = 70.000 \)

To solve, multiply equation 1 by 5 and equation 2 by 4 to eliminate the variables more easily:
- \( 100x + 150y = 350.000 \)
- \( 100x + 80y = 280.000 \)

Now, subtract equation 2 from equation 1:
\[
(100x + 150y) - (100x + 80y) = 350.000 - 280.000
\]
\[
70y = 70.000
\]
\[
y = 1.000
\]

Substitute \( y = 1.000 \) into equation 1:
\[
20x + 30(1.000) = 70.000
\]
\[
20x + 30.000 = 70.000
\]
\[
20x = 40.000
\]
\[
x = 2.000
\]

So, the price of one coin I is **Rp2.000**, and the price of one coin II is **Rp1.000**.

---

### Problem 4:
We need to determine the original volume of orange juice and water.

Let:
- \( o \) be the original volume of orange juice,
- \( w \) be the original volume of water.

- The original mixture contains 300 mL of juice, made of orange juice and water.
- Anita adds 20% more orange juice and 50% more water, and the final volume becomes 420 mL.

We know:
\[
o + w = 300
\]
\[
1.2o + 1.5w = 420
\]

Substitute \( w = 300 - o \) into the second equation:
\[
1.2o + 1.5(300 - o) = 420
\]
\[
1.2o + 450 - 1.5o = 420
\]
\[
-0.3o + 450 = 420
\]
\[
-0.3o = -30
\]
\[
o = 100
\]

Substitute \( o = 100 \) into the first equation:
\[
100 + w = 300
\]
\[
w = 200
\]

So, the original volume of orange juice is **100 mL**, and the original volume of water is **200 mL**.

---

Would you like any further explanation or details on any part of this solution?

Here are 5 related questions you could explore:
1. How would the equations change if the total cost for 1 pineapple and 4 apples were given instead?
2. What if the table had a different height? How would it affect the plant’s height?
3. How can we verify the price of the coins using a different method?
4. How much juice would there be if Anita added 30% more orange juice instead?
5. What is the total percentage of water in the final mixture?

**Tip:** When solving simultaneous linear equations, subtraction or substitution can simplify the system to find the unknowns efficiently.

With the given table, determine the unknown values using one of the methods provided for solving simultaneous linear equations (SPLDV).

Learn how to solve various word problems involving simultaneous linear equations, including determining the price of fruits, calculating heights, coin value analysis, and juice composition. Perfect for students in Grades 8-10 learning algebraic methods.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation