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 + 2 ÷ 25 + 5 - 10 = ?

Introduction / Context:
This problem checks your ability to decode symbol substitutions and then evaluate an expression using standard arithmetic precedence. The key skill is to first replace each symbol with its actual meaning, and only then calculate.

Given Data / Assumptions:

• '+' represents multiplication (*).
• '-' represents addition (+).
• 'x' represents division (/).
• '÷' represents subtraction (-).
• Use BODMAS/precedence: multiplication and division before addition and subtraction.

Concept / Approach:
Rewrite the entire expression by replacing each operator with its true operation. Then evaluate the rewritten expression normally. Do not mix coded precedence with real precedence.

Step-by-Step Solution:
Original: 80 + 2 ÷ 25 + 5 - 10 Replace '+' with *: 80 * 2 ÷ 25 * 5 - 10 (not correct yet because ÷ and - also change) Now apply all mappings correctly: 80 + 2 becomes 80 * 2 2 ÷ 25 becomes 2 - 25 25 + 5 becomes 25 * 5 5 - 10 becomes 5 + 10 So decoded expression is: 80 * 2 - 25 * 5 + 10 Compute: 80 * 2 = 160 Compute: 25 * 5 = 125 Now: 160 - 125 + 10 = 45

Verification / Alternative check:
Quick check: since 25 * 5 = 125 cancels most of 160, the result should be near 35, and adding 10 gives 45. This matches the computed value.

Why Other Options Are Wrong:
36: would come from incorrect operator replacement or order. 35: often from stopping at 160 - 125. 98: usually from treating + as + instead of *. 40: from partial precedence mistakes.

Common Pitfalls:
Replacing only some operators, evaluating before decoding, or applying wrong precedence to the coded symbols are common errors.

Final Answer:
45