In a certain code language, the symbol plus represents multiplication, the minus sign represents addition, the symbol x represents division and the division sign represents subtraction. What is the value of the coded expression 550 x 22 - 24 + 3 ?

Introduction / Context:
This problem involves decoding an arithmetic expression in which the usual operators have been reassigned new meanings. Once each symbol has been translated back into its real mathematical operation, we must evaluate the resulting expression using correct precedence rules. This type of coding question checks attention to detail and understanding of basic arithmetic.

Given Data / Assumptions:

• Plus represents multiplication.
• Minus represents addition.
• The symbol x represents division.
• The division sign represents subtraction.
• The coded expression is 550 x 22 - 24 + 3.
• We must apply standard precedence: perform all multiplication and division before addition and subtraction.

Concept / Approach:
The strategy is to rewrite the coded expression using the real arithmetic symbols. In other words, wherever we see x we interpret it as division, wherever we see plus we interpret it as multiplication, and so on. After translating, we handle division and multiplication first, then work through addition and subtraction from left to right. Careful decoding is essential because a single misread symbol changes the entire result.

Step-by-Step Solution:
Step 1: Translate 550 x 22. Since x represents division, this becomes 550 ÷ 22. Step 2: Translate the minus sign. Minus represents addition, so - 24 becomes + 24. Step 3: Translate the plus sign. Plus represents multiplication, so + 3 becomes × 3. Step 4: The decoded expression is therefore 550 ÷ 22 + 24 × 3. Step 5: Apply precedence. First compute 550 ÷ 22. Step 6: 550 ÷ 22 equals 25. Step 7: Next compute 24 × 3, which equals 72. Step 8: Now perform the remaining addition: 25 + 72 = 97. Step 9: Thus the value of the coded expression is 97.

Verification / Alternative check:
To verify, we can recompute 550 ÷ 22 using approximate mental arithmetic to confirm it is 25, and 24 × 3 is clearly 72. Their sum is 97. Since there are no further operations, and all symbol meanings have been correctly applied, the result is consistent and reliable.

Why Other Options Are Wrong:
The other values 91, 77 and 71 come from various decoding mistakes. For instance, treating x as multiplication or interpreting plus as addition instead of multiplication would lead to a different sequence of operations and an incorrect answer. Ignoring operator precedence and computing strictly from left to right can also produce wrong totals. Only 97 fits a correct decoding followed by proper arithmetic.

Common Pitfalls:
Common mistakes include forgetting that the symbol meanings have been swapped, especially for plus and minus, and failing to handle multiplication and division before addition and subtraction. Writing the decoded expression clearly with standard operators before performing any calculations is an effective way to avoid such errors in timed tests.

Final Answer:
After decoding each symbol and applying operator precedence, the coded expression evaluates to 97.