In a coded arithmetic puzzle, the symbol ÷ stands for subtraction, the symbol - stands for addition, the symbol x stands for division and the symbol + stands for multiplication. Using these substituted meanings, which one of the following equations becomes numerically correct?

Introduction / Context:
This question again tests comfort with coded arithmetic, a popular topic in verbal and logical reasoning. Each familiar arithmetic symbol has been assigned a new meaning, and we must determine which equation remains valid when those new meanings are used. Because every option has the same left side and differs only in the right side result, our task is essentially to evaluate the left side under the new rules and then match the correct numerical value among the options. This requires careful symbol replacement and strict application of arithmetic precedence.

Given Data / Assumptions:

• Symbol ÷ means subtraction.
• Symbol - means addition.
• Symbol x means division.
• Symbol + means multiplication.
• All options share the same left side expression: 35 ÷ 4 - 25 x 5 + 5.
• We must evaluate that expression after substitution and then compare it to the right side numbers.

Concept / Approach:
The approach is to first rewrite the coded expression by replacing each operator with its real meaning. Once we have a standard arithmetic expression, we can evaluate it using the usual precedence where multiplication and division are done before addition and subtraction. Because the same expression is reused in every option, we only need to do the calculation once. The correct option is simply the one where the right side equals the computed result. This makes the problem straightforward if we proceed methodically and avoid mixing up the operator meanings.

Step-by-Step Solution:
Step 1: Start with the left side: 35 ÷ 4 - 25 x 5 + 5. Step 2: Substitute each symbol: ÷ becomes subtraction, - becomes addition, x becomes division and + becomes multiplication. Step 3: After substitution, the expression becomes 35 - 4 + 25 / 5 * 5. Step 4: Apply precedence. First compute the division 25 / 5 = 5. Step 5: Then multiply: 5 * 5 = 25. The expression now is 35 - 4 + 25. Step 6: Perform subtraction and addition from left to right: 35 - 4 = 31, then 31 + 25 = 56. Step 7: The correct value of the left side under the coded rules is therefore 56.

Verification / Alternative check:
Once we know that the evaluated left side is 56, it is enough to look at the options and select the one that matches this value on the right side. Only option D claims that the entire equation equals 56. Options A, B, C and E all assert different numerical results that do not correspond to the actual computed value. Since the coding rule is fixed and we have followed arithmetic precedence correctly, there is no ambiguity in this result.

Why Other Options Are Wrong:
Option A suggests that the expression equals 28, which would require a much smaller positive contribution from the division and multiplication part. Option B claims 61, option C claims 41 and option E claims 36; none of these numbers match the exact value 56 obtained after proper substitution and calculation. These values are likely based on common mistakes such as reversing subtraction and addition or ignoring precedence, and they serve as distractors for hasty solvers.

Common Pitfalls:
Many learners mistakenly treat the operators as if they still had their usual meanings and directly compute 35 ÷ 4 as ordinary division. Others forget to respect the order of operations after substitution and simply calculate from left to right. Another error is to misread the mapping of a single symbol, for example treating x as multiplication instead of division in this puzzle. Writing out the substituted expression clearly before performing any numeric work is the best way to avoid such slips.

Final Answer:
Under the given coded meanings of the symbols, the expression evaluates to 56, so the correct equation is 35 ÷ 4 - 25 x 5 + 5 = 56.