`{:(" 3A"),("+25"),(--),(" B2"),(--):}`

Answer

To solve the problem step by step, we need to analyze the equation given in the question: \(3A + 25 = B2\).

1. **Understanding the Equation**:
- Here, \(3A\) represents a number formed by the digit 3 followed by the digit A.
- \(B2\) represents a number formed by the digit B followed by the digit 2.
- We need to find the values of A and B.

2. **Setting Up the Equation**:
- The number \(3A\) can be expressed as \(30 + A\) (since A is the units digit).
- The number \(B2\) can be expressed as \(10B + 2\) (since 2 is the units digit).
- Therefore, we can rewrite the equation as:
\[ 30 + A + 25 = 10B + 2 \]
- Simplifying this gives:
\[ 55 + A = 10B + 2 \]

3. **Rearranging the Equation**:
- Rearranging the equation to isolate A gives:
\[ A = 10B + 2 - 55 \]
- This simplifies to:
\[ A = 10B - 53 \]

4. **Finding Possible Values for A and B**:
- Since A is a single digit (0 to 9), we need to find values of B such that \(10B - 53\) is a valid single digit.
- Let's evaluate possible values of B:
- If \(B = 6\):
\[ A = 10(6) - 53 = 60 - 53 = 7 \]
- If \(B = 7\):
\[ A = 10(7) - 53 = 70 - 53 = 17 \quad (\text{not valid, since A must be a single digit}) \]
- Therefore, the only valid solution is \(B = 6\) and \(A = 7\).

5. **Final Values**:
- The values we found are:
- \(A = 7\)
- \(B = 6\)

### Summary of the Solution:
- The values of A and B are:
- \(A = 7\)
- \(B = 6\)