Rahul had some pencils, pens, and markers in the ratio 5 : 3 : 2. The number of markers was 2/3 of the number of crayons. What is the ratio of the number of pencils to pens to markers to crayons?

We are given the ratio of pencils, pens, and markers in the ratio \( 5 : 3 : 2 \), and the additional information that the number of markers is \( \frac{2}{3} \) of the number of crayons.

Let’s break it down step by step:

1. **Define the variables:**
   - Let the number of pencils, pens, and markers be \( 5x \), \( 3x \), and \( 2x \), respectively, where \( x \) is a common multiplier.
   - Let the number of crayons be \( y \).

2. **Relating markers to crayons:**
   The number of markers is \( \frac{2}{3} \) of the number of crayons. Therefore, we can write the relationship as:
   \[
   2x = \frac{2}{3}y
   \]

3. **Solve for \( y \) in terms of \( x \):**
   Multiply both sides of the equation by 3 to eliminate the fraction:
   \[
   3(2x) = 2y
   \]
   \[
   6x = 2y
   \]
   Divide both sides by 2:
   \[
   3x = y
   \]
   So, the number of crayons is \( y = 3x \).

4. **Final ratio:**
   Now, we have the number of pencils, pens, markers, and crayons as:
   - Pencils: \( 5x \)
   - Pens: \( 3x \)
   - Markers: \( 2x \)
   - Crayons: \( 3x \)

   Therefore, the ratio of pencils to pens to markers to crayons is:
   \[
   5x : 3x : 2x : 3x = 5 : 3 : 2 : 3
   \]

Thus, the ratio of pencils to pens to markers to crayons is \( \boxed{5 : 3 : 2 : 3} \).

Would you like further clarification or additional details?

Here are 5 related questions for deeper understanding:
1. If Rahul had 30 markers, how many crayons did he have?
2. How would the ratio change if the number of markers was half the number of crayons?
3. If the total number of items was 130, how many pencils, pens, markers, and crayons were there?
4. Can you derive the ratio of pencils to crayons directly?
5. If the ratio of pens to crayons was \( 1 : 1 \), how would the relationship between pencils and pens change?

**Tip:** Always start by assigning variables based on given ratios, then use additional conditions to find relationships between them.

Explore how to solve a ratio problem involving pencils, pens, markers, and crayons. The solution uses key algebraic concepts to find the relationship between the number of markers and crayons, leading to a final ratio of 5:3:2:3. Suitable for students in 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