https://file.aiquickdraw.com/mathbot/file/1726464422349g373ivs4.jpg

The problem states:

"If 20% of \( X \) = 30% of \( Y \), then \( X : Y \) = ?"

### Step-by-step solution:

1. First, express the given condition mathematically:
   \[
   20\% \text{ of } X = 30\% \text{ of } Y
   \]
   This can be written as:
   \[
   0.20X = 0.30Y
   \]

2. Now, divide both sides by 0.30 to isolate \( Y \):
   \[
   \frac{0.20X}{0.30} = Y
   \]
   Simplifying the fraction:
   \[
   \frac{2X}{3} = Y
   \]

3. To find the ratio \( X : Y \), express \( X \) in terms of \( Y \):
   \[
   X = \frac{3}{2}Y
   \]

4. Therefore, the ratio \( X : Y \) is:
   \[
   X : Y = \frac{3}{2} : 1
   \]
   Or simply:
   \[
   X : Y = 3 : 2
   \]

### Final answer:
The ratio \( X : Y = 3 : 2 \).

Would you like further details or have any questions?

Here are some related questions for further practice:
1. If 40% of \( X \) equals 50% of \( Y \), what is \( X : Y \)?
2. If \( X : Y = 5 : 3 \), what percentage of \( X \) equals 40% of \( Y \)?
3. How would the ratio change if 10% of \( X \) equals 15% of \( Y \)?
4. If \( X = 60 \) and \( Y = 40 \), what is the ratio of \( X \) to \( Y \)?
5. Can you generalize the rule for solving ratios given percentages of two variables?

**Tip**: Always express percentage problems as equations to simplify solving ratios.

Learn how to solve the ratio problem where 20% of X equals 30% of Y. The solution includes detailed steps involving percentages and ratios, ideal 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