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Replace A,B,C by suitable numberals: (...

Replace A,B,C by suitable numberals:
`({:(," "57A),(,""-CB8):})/(" "293)`

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To solve the problem, we need to replace A, B, and C with suitable numerals in the expression `({:(," "57A),(,""-CB8):})/(" "293)`. Let's break down the steps to find the values of A, B, and C. ### Step-by-Step Solution: 1. **Understand the Expression**: The expression can be interpreted as: \[ \frac{(57A - CB8)}{293} \] We need to find values for A, B, and C such that this expression holds true. 2. **Analyze the Units Place**: Start with the units place of the numbers involved. The units place of `57A` is A, and the units place of `CB8` is 8. We need to find A such that: \[ A - 8 \equiv 3 \mod 10 \] This means that A must be 1 because: \[ 1 - 8 = -7 \equiv 3 \mod 10 \] (We can think of this as borrowing 1 from the next column.) **Hint**: Check the units place first to determine A. 3. **Determine the Tens Place**: Now, consider the tens place. The tens place of `57A` is 7, and we need to subtract the tens place of `CB8` which is B. Since we borrowed 1 from the hundreds place, we have: \[ 6 - B \equiv 9 \mod 10 \] This means: \[ 6 - B = 9 \implies B = 6 - 9 = -3 \quad \text{(not possible)} \] Instead, we should consider the carry from the hundreds place: \[ 16 - B = 9 \implies B = 16 - 9 = 7 \] **Hint**: Use the carry from the previous column to adjust the subtraction. 4. **Determine the Hundreds Place**: Now, for the hundreds place, we have: \[ 5 - C \equiv 2 \mod 10 \] This means: \[ 5 - C = 2 \implies C = 5 - 2 = 3 \] **Hint**: Solve for C using the hundreds place after accounting for any carry. 5. **Final Values**: After solving the above equations, we find: - A = 1 - B = 7 - C = 3 ### Conclusion: The suitable numerals to replace A, B, and C are: - A = 1 - B = 7 - C = 3
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