A and B share some marbles in the ratio 4 : 5. If B gets 10 marbles more than A, then what is A's share?

Answer

To solve the problem of how many marbles A has when A and B share marbles in the ratio of 4:5 and B has 10 more marbles than A, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ratio**:
- A and B share marbles in the ratio 4:5. This means for every 4 parts A gets, B gets 5 parts.

2. **Assign Variables**:
- Let the number of marbles A gets be represented as \( 4x \).
- Let the number of marbles B gets be represented as \( 5x \).
- Here, \( x \) is a common multiplier.

3. **Setting Up the Equation**:
- According to the problem, B gets 10 more marbles than A. This can be expressed mathematically as:
\[ 5x = 4x + 10 \]

4. **Solving the Equation**:
- To find the value of \( x \), we can simplify the equation:
\[ 5x - 4x = 10 \]
\[ x = 10 \]

5. **Calculating A's Share**:
- Now that we have the value of \( x \), we can find A's share:
\[ A's \, share = 4x = 4 \times 10 = 40 \]

6. **Conclusion**:
- Therefore, A's share of the marbles is **40 marbles**.