If (−) stands for division, (+) stands for multiplication, (÷) stands for subtraction and (×) stands for addition, which one of the following equations is actually correct?

Introduction / Context:
This problem uses a code for arithmetic operations. Instead of using the usual meanings of +, −, ×, and ÷, each symbol is redefined. You must determine which of the provided statements becomes a numerically correct equality after decoding each symbol and applying standard arithmetic rules. This tests careful interpretation and systematic checking.

Given Data / Assumptions:

- "−" stands for division.
- "+" stands for multiplication.
- "÷" stands for subtraction.
- "×" stands for addition.
- We are to choose from the given options which equation, after decoding, is actually true.
- Once decoded, standard precedence of operations (multiplication and division before addition and subtraction) must be followed.

Concept / Approach:
For each option, replace the coded operators with their actual meanings, then simplify the left-hand side and compare it with the right-hand side. Because there are only four options, a direct check is efficient. The equation that results in equal values on both sides is the correct choice.

Step-by-Step Solution:
Consider option A: 100+5−10×250÷200 = 100. Decode each symbol using the given mapping. "+" stands for multiplication, so 100+5 becomes 100 × 5. "−" stands for division, so −10 becomes ÷ 10. "×" stands for addition, so 10×250 becomes 10 + 250. "÷" stands for subtraction, so 250÷200 becomes 250 − 200. Putting this together, the left-hand side becomes: 100 × 5 ÷ 10 + 250 − 200. Step 1: Apply multiplication and division from left to right. 100 × 5 = 500. 500 ÷ 10 = 50. The expression now is: 50 + 250 − 200. Step 2: Perform addition and subtraction. 50 + 250 = 300. 300 − 200 = 100. Thus the left-hand side simplifies to 100, which equals the right-hand side 100.

Verification / Alternative check:
We can briefly check one of the other options to see that it fails. For example, option B decodes to 200 × 10 ÷ 20 + 200 − 100. Simplifying gives 200 × 10 = 2000, 2000 ÷ 20 = 100, and then 100 + 200 − 100 = 200, which does not equal 150. Similar checks show that options C and D also do not balance, so option A is uniquely correct.

Why Other Options Are Wrong:

- Option B simplifies to a value different from the right-hand side, as shown above.
- Option C gives a left-hand side that does not equal 50 after correct decoding.
- Option D also leads to a mismatch between the two sides of the equation.

In every incorrect option, either the left-hand side is not equal to the right-hand side, or a misinterpretation of symbols would be required to force equality, which is not allowed.

Common Pitfalls:
Learners may forget to decode every symbol, or they may revert to the original meanings of the operators out of habit. Another source of errors is disregarding the precedence of multiplication and division, which can alter the final result. Working slowly and rewriting the decoded expression clearly makes it easier to avoid such mistakes.

Final Answer:
The only equation that becomes numerically correct after decoding the signs is 100+5−10×250÷200 = 100 (option A).