https://file.aiquickdraw.com/mathbot/file/1725871263080r2emp5lw.jpg

The problem can be solved using algebra by defining variables for the prices of a pencil, pen, and book. Here's how we can approach the solution:

Let:
- \( x \) = price of a pencil (in rupees)
- \( y \) = price of a pen (in rupees)
- \( z \) = price of a book (in rupees)

### From the problem statement:
1. **The price of a pen is 2 times the price of a pencil:**
   \[
   y = 2x
   \]

2. **The price of a book is 10 times the price of a pencil:**
   \[
   z = 10x
   \]

3. **The student bought 5 pencils, 10 pens, and 2 books for a total of 135 rupees:**
   \[
   5x + 10y + 2z = 135
   \]

### Substituting \( y = 2x \) and \( z = 10x \) into the total cost equation:

\[
5x + 10(2x) + 2(10x) = 135
\]

This simplifies to:

\[
5x + 20x + 20x = 135
\]

\[
45x = 135
\]

\[
x = \frac{135}{45} = 3
\]

### Now that we know \( x = 3 \), we can calculate the price of a pen and the price of a book:
- Price of a pencil: \( x = 3 \) rupees
- Price of a pen: \( y = 2x = 2(3) = 6 \) rupees
- Price of a book: \( z = 10x = 10(3) = 30 \) rupees

### Final answers:
- (a) The price of a pencil is 3 rupees.
- (b) The price of a pen is 6 rupees.
- (c) The price of a book is 30 rupees.

Let me know if you want more details on the solution or have any questions.

---

**Follow-up Questions:**
1. How would the total cost change if the price of the book was only 8 times the price of a pencil?
2. What would the total cost be if the student bought 2 fewer pens?
3. What if the price of a pen was 3 times the price of a pencil?
4. How would you set up the equation if the number of pencils purchased was unknown?
5. Can you find another way to verify the total cost without substituting directly into the equation?

**Tip:** When solving word problems, always define your variables clearly and check if the final solution satisfies all the conditions given in the problem.

The price of a pen is 2 times the price of a pencil. The price of a book is 10 times the price of a pencil. A student bought 5 pencils, 10 pens, and 2 books from a shop for rupees 135. (a) What is the price of a pencil? (b) What is the price of a pen? (c) What is the price of a book?

Solve this algebra problem where the price of a pen is 2 times that of a pencil and the price of a book is 10 times the price of a pencil. Learn how to use substitution in linear equations to find the prices. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation