https://file.aiquickdraw.com/mathbot/file/17267198608262ih3vclx.jpg

To solve the problem, let's use variables to represent the prices of a pencil and a notebook.

Let:
- \( p \) = price of a pencil
- \( b \) = price of a notebook

From the problem, we have the following equations:

1. \( 2p + 4b = 11,000 \) (Equation 1)
2. \( 6p + 2b = 13,000 \) (Equation 2)

We need to find the price for 3 pencils and 2 notebooks, which is represented by \( 3p + 2b \).

### Step 1: Solve Equations 1 and 2
**Equation 1:**
\[
2p + 4b = 11,000
\]
Divide the whole equation by 2:
\[
p + 2b = 5,500 \quad \text{(Equation 3)}
\]

**Equation 2:**
\[
6p + 2b = 13,000
\]
Divide the whole equation by 2:
\[
3p + b = 6,500 \quad \text{(Equation 4)}
\]

### Step 2: Use Equation 3 to Express \( p \)
From Equation 3:
\[
p = 5,500 - 2b
\]

### Step 3: Substitute \( p = 5,500 - 2b \) into Equation 4
\[
3(5,500 - 2b) + b = 6,500
\]
\[
16,500 - 6b + b = 6,500
\]
\[
16,500 - 5b = 6,500
\]
\[
-5b = 6,500 - 16,500
\]
\[
-5b = -10,000
\]
\[
b = 2,000
\]

### Step 4: Find \( p \) Using \( b = 2,000 \)
\[
p = 5,500 - 2(2,000)
\]
\[
p = 5,500 - 4,000
\]
\[
p = 1,500
\]

### Step 5: Calculate \( 3p + 2b \)
\[
3p + 2b = 3(1,500) + 2(2,000)
\]
\[
3p + 2b = 4,500 + 4,000
\]
\[
3p + 2b = 8,500
\]

So, the price for 3 pencils and 2 notebooks is **Rp8,500.00**, which corresponds to option C.

Would you like more details or have any other questions? Here are some additional questions for further practice:

1. How would the answer change if the price of one pencil increased by Rp500?
2. What is the price of 5 pencils and 3 notebooks?
3. How would you solve the problem using the substitution method from the beginning?
4. Can you express the cost in terms of one variable only?
5. What is the combined cost of 10 pencils and 6 notebooks?

**Tip:** Always simplify equations first to reduce complexity in problem-solving.

Harga 2 pensil dan 4 buku tulis Rp11.000,00 sedangkan harga 6 pensil dan 2 buku tulis Rp13.000,00, maka harga 3 pensil dan 2 buku tulis adalah ....

Learn how to calculate the price of 3 pencils and 2 notebooks using systems of equations and substitution. Understand how to simplify equations and solve for variables. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation