In a certain code language, the arithmetic symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operators, what is the value of 45 x 5 + 2 - 20?

Introduction:
This operator coding problem asks us to evaluate an arithmetic expression in which each familiar symbol has been reassigned a new meaning. The correct solution requires decoding every operator in the expression 45 x 5 + 2 - 20 and then applying normal arithmetic precedence rules. The question checks both symbol translation skills and basic calculation accuracy.

Given Data / Assumptions:
The redefined meanings are:
1) "+" represents multiplication.
2) "-" represents addition.
3) "x" represents division.
4) "÷" represents subtraction (not used directly here).
The coded expression is 45 x 5 + 2 - 20. After decoding, we apply standard precedence: division and multiplication first, then addition and subtraction from left to right.

Concept / Approach:
The most robust approach is a two step process: first, convert the coded symbols into actual operations; second, compute the final value carefully. It is important not to mix the visual symbol with its usual arithmetic meaning but to always use the provided mapping. Once rewritten, the expression looks familiar and can be evaluated as usual.

Step-by-Step Solution:
Step 1: Replace the "x" symbol with division. Thus 45 x 5 becomes 45 / 5.Step 2: Replace the "+" symbol with multiplication. So + 2 becomes * 2.Step 3: Replace the "-" symbol with addition. So - 20 becomes + 20.Step 4: The decoded expression becomes 45 / 5 * 2 + 20.Step 5: Apply arithmetic precedence. First evaluate 45 / 5 = 9.Step 6: Then evaluate 9 * 2 = 18.Step 7: Now the expression is 18 + 20.Step 8: Add the numbers: 18 + 20 = 38.Step 9: Therefore, the value of the given coded expression is 38.

Verification / Alternative check:
We can rephrase the decoded expression as "forty five divided by five multiplied by two plus twenty". This clearly evaluates to 9 times 2 plus 20, or 18 plus 20, which is 38. No extra brackets or alternative interpretations are implicit, so the answer is consistent.

Why Other Options Are Wrong:
The value 17 or 28 could arise from treating one of the operations as subtraction instead of multiplication or addition. The value 81 might come from mistakenly doing 45 * 5 then combining with 2 and 20 in an ad hoc manner. The value 64 would require ignoring division or misapplying operator precedence. None of these approaches respects both the redefined operators and standard evaluation order.

Common Pitfalls:
Common mistakes include leaving one operator untranslated, such as still reading "-" as minus, or performing operations strictly left to right without handling division and multiplication first. Writing the fully translated expression before starting the calculation helps maintain clarity and avoid confusion.

Final Answer:
Using the given coded meanings of the operators, the expression evaluates to 38.