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 and standard precedence, what is the correct value of: 75 - 5 + 25 ÷ 125 = ?

Introduction / Context:
This question checks your ability to decode operator substitutions and then correctly evaluate the resulting arithmetic expression. The symbols shown in the expression do not represent their usual operations, so decoding is mandatory before calculating.

Given Data / Assumptions:

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

Concept / Approach:
Replace each operator according to the mapping while keeping the operator positions the same. Then evaluate using standard precedence (multiplication/division before addition/subtraction).

Step-by-Step Solution:
Original: 75 - 5 + 25 ÷ 125 Decode each operator at its position: '-' becomes +, so: 75 + 5 ... '+' becomes *, so between 5 and 25 it becomes: * 25 '÷' becomes -, so between 25 and 125 it becomes: - 125 Decoded expression: 75 + 5 * 25 - 125 Compute multiplication: 5 * 25 = 125 Now: 75 + 125 - 125 = 75

Verification / Alternative check:
After decoding, the expression becomes 75 + (125 - 125). Since (125 - 125) = 0, the result must be 75. This provides a quick confirmation.

Why Other Options Are Wrong:
10 or 5: come from wrong decoding of + as + or ÷ as /. 3: typically from dividing 75 by something incorrectly. 80: comes from doing 75 + 5 without applying multiplication and subtraction correctly.

Common Pitfalls:
Evaluating before decoding, ignoring precedence (doing 75+5 first then multiplying), or mixing up which symbol maps to subtraction are common mistakes.

Final Answer:
75