The ratio of the number of marbles in your ARB to jersey is 2 to 5 to 4. There are 12 more marbles in jersey than there are in how many marbles should be replaced from Darby to JA so that jars and B have the same number of marbles?

Let's break down the problem step-by-step.

### Step 1: Defining Variables
Let the number of marbles in ARB, Jersey, and Darby be represented by the variables \(A\), \(J\), and \(D\), respectively. According to the given ratio, we have:
\[
A : J : D = 2 : 5 : 4
\]

Let's introduce a common multiplier \(x\) to represent the number of marbles:
\[
A = 2x, \quad J = 5x, \quad D = 4x
\]

### Step 2: Condition Involving Jersey and ARB
The problem states there are 12 more marbles in Jersey than in ARB:
\[
J = A + 12
\]
Substitute \(A = 2x\) and \(J = 5x\):
\[
5x = 2x + 12
\]
Solving for \(x\):
\[
3x = 12 \quad \Rightarrow \quad x = 4
\]

### Step 3: Calculating Initial Number of Marbles
Now we can find the initial number of marbles in each jar:
\[
A = 2x = 2(4) = 8
\]
\[
J = 5x = 5(4) = 20
\]
\[
D = 4x = 4(4) = 16
\]

### Step 4: Finding Marbles to be Transferred
The problem asks how many marbles should be transferred from Darby to ARB so that ARB and Darby have the same number of marbles. 

Let's say we transfer \(y\) marbles from Darby to ARB. The new number of marbles in each jar will be:

For ARB:
\[
A_{\text{new}} = 8 + y
\]

For Darby:
\[
D_{\text{new}} = 16 - y
\]

Setting them equal, since they need to have the same number:
\[
8 + y = 16 - y
\]

Solving for \(y\):
\[
2y = 8 \quad \Rightarrow \quad y = 4
\]

### Final Answer
So, 4 marbles should be transferred from Darby to ARB for both jars to have the same number of marbles.

Would you like more details or have any questions?

#### Related Questions:
1. What is the total number of marbles in all three jars after the transfer?
2. If 3 marbles were added to each jar, what would the new ratio be?
3. How many marbles would each jar have if the ratio changed to 3:4:5?
4. What is the percentage increase in the number of marbles in ARB after the transfer?
5. If 6 marbles were removed from Jersey, how many would each jar have then?

**Tip:** Always double-check ratios and conditions given in word problems by substituting values to ensure your equations and calculations are correct.

Learn how to solve a marbles transfer problem involving ratios and equations. The problem asks how many marbles should be transferred from Darby to ARB to make the number of marbles equal. Suitable for Grades 6-8, this example demonstrates the use of algebraic equations to find solutions to real-world problems.

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