A, B and C are integers and represent the digits of the numbers given below.If 6ABC + 6BC + 7C = 6670,then B = ?

To solve this problem, we need to break it down into smaller steps:

1. First, let's rewrite the equation in a more understandable format. The problem states that 6ABC + 6BC + 7C = 6670. This can be rewritten as 6000A + 600B + 6C + 600B + 60C + 7C = 6670.

2. Combine like terms: 6000A + 1200B + 73C = 6670.

3. Divide the entire equation by 1000 to simplify: 6A + 1.2B + 0.073C = 6.67.

4. Now, we know that A, B, and C are integers. This means that 0.073C must also be an integer. The only way for this to happen is if C = 0.

5. Substitute C = 0 into the equation: 6A + 1.2B = 6.67.

6. Now, we know that A and B are integers. This means that 6A must be an integer and therefore, A = 1.

7. Substitute A = 1 into the equation: 6 + 1.2B = 6.67.

8. Solve for B: 1.2B = 0.67. Divide both sides by 1.2 to get B = 0.67 / 1.2 = 0.558333.

9. However, we know that B must be an integer. Therefore, the only possible value for B is 0.

So, B = 0.