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To solve the given problem, let's break down the information provided:

1. Each red box has a height of 12 cm.
2. Each green box has a height of 25 cm.
3. We need to stack the red and green boxes to equal heights.
4. The total number of boxes (red + green) must be more than 20.
5. We need to find the minimum number of red boxes.

Let's denote:
- \( r \) as the number of red boxes,
- \( g \) as the number of green boxes.

For the stacks to be of equal height:
\[ 12r = 25g \]

This means:
\[ r = \frac{25}{12}g \]

Since \( r \) must be an integer, \( g \) must be a multiple of 12. Let's find the smallest possible \( g \) such that the total number of boxes \( r + g \) is more than 20.

### Step-by-Step Solution:
1. Let’s start with the smallest multiple of 12 and check:
   - If \( g = 12 \):
     \[ r = \frac{25}{12} \times 12 = 25 \]
     \[ r + g = 25 + 12 = 37 \]
     Since 37 is more than 20, this solution is valid.

Therefore, the smallest number of red boxes \( r \) is 25 when the total number of boxes exceeds 20.

Thus, the minimum number of red boxes is:

\[ \boxed{25} \]

Would you like any further details or explanations?

Here are 5 questions you might ask next:
1. How to solve equations involving multiple variables?
2. How to simplify fractions in mathematical problems?
3. What are common strategies for solving word problems in algebra?
4. How to identify and use least common multiples (LCM) in equations?
5. Can you explain how to set up equations from a word problem?

**Tip:** When solving word problems, always start by defining your variables and writing down the relationships given in the problem as equations. This helps in organizing information and finding the solution systematically.

Learn how to minimize the number of red boxes in a stacking problem where each red box has a height of 12 cm and each green box has a height of 25 cm. This problem involves setting up and solving a proportion equation to find the minimum number of red boxes required to satisfy given conditions. Suitable for students in Grades 7-9.

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