A box contained 3 times as many red marbles as blue marbles. After 40 red marbles were removed, there was twice as many blue marbles as red marbles. How many marbles were there in the end?

Let's break down the problem step by step:

1. **Initial Setup:**
   - Let the number of blue marbles initially be \( x \).
   - Therefore, the number of red marbles initially is \( 3x \) (since there are 3 times as many red marbles as blue marbles).

2. **After Removing Red Marbles:**
   - 40 red marbles are removed, so the number of red marbles left is \( 3x - 40 \).
   - The problem states that now the number of blue marbles is twice the number of red marbles. Thus, we have the equation:
   \[
   x = 2(3x - 40)
   \]

3. **Solving the Equation:**
   - Expanding and simplifying the equation:
   \[
   x = 6x - 80
   \]
   - Bring all terms involving \( x \) to one side:
   \[
   80 = 5x
   \]
   - Solving for \( x \):
   \[
   x = 16
   \]

4. **Determine the Number of Marbles in the End:**
   - The initial number of blue marbles was \( x = 16 \).
   - The initial number of red marbles was \( 3x = 48 \).
   - After removing 40 red marbles, the number of red marbles left is \( 48 - 40 = 8 \).
   - So, the total number of marbles in the end is the sum of the remaining blue and red marbles:
   \[
   16 + 8 = 24
   \]

Therefore, there were **24 marbles** in the end.

Would you like further details or have any questions?

Here are some related questions to consider:

1. What if there were 5 times as many red marbles as blue marbles initially?
2. How would the result change if 60 red marbles were removed instead of 40?
3. What if the box originally contained 10 times as many red marbles as blue marbles?
4. How would the solution differ if instead of blue, there were green marbles?
5. Can this problem be solved using a different method, such as a graphical approach?

**Tip:** When solving word problems, it's helpful to translate the problem into algebraic equations step by step, as this helps in organizing the information systematically.

Explore the solution to a math word problem involving marbles and removal. Learn how to solve the problem step-by-step with detailed explanations. Suitable for Grades 7-9.

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