In a certain code language, the operator symbols are redefined as follows: '+' means multiplication (*), '-' means addition (+), 'x' means division (/), and '÷' means subtraction (-). Using this decoding, what is the correct value of: 80 x 16 ÷ 4 + 2 - 8 = ?

Introduction / Context:
This question checks decoding of swapped mathematical operators and correct evaluation using normal precedence rules. The expression must be translated into standard operations first, and only then computed.

Given Data / Assumptions:

• '+' represents multiplication (*).
• '-' represents addition (+).
• 'x' represents division (/).
• '÷' represents subtraction (-).
• Use standard precedence after decoding.

Concept / Approach:
Convert each coded operator to its real meaning. Then compute the decoded expression using multiplication/division before addition/subtraction.

Step-by-Step Solution:
Original: 80 x 16 ÷ 4 + 2 - 8 Decode operators one by one: x means /, so: 80 / 16 ÷ means -, so between 16 and 4 it becomes: - 4 + means *, so between 4 and 2 it becomes: * 2 - means +, so between 2 and 8 it becomes: + 8 Decoded expression: 80 / 16 - 4 * 2 + 8 Compute division: 80 / 16 = 5 Compute multiplication: 4 * 2 = 8 Now: 5 - 8 + 8 = 5

Verification / Alternative check:
Notice that - (4*2) + 8 cancels out to 0, leaving only 80/16 = 5. This confirms the answer quickly.

Why Other Options Are Wrong:
64: comes from treating x as multiplication. 11: from incorrect decoding of - as subtraction. 30: from computing without precedence or wrong mapping. 13: from partial cancellation errors.

Common Pitfalls:
Evaluating the coded expression directly, forgetting to decode every operator, or doing subtraction before multiplication causes incorrect results.

Final Answer:
5