In a certain code language, the arithmetic symbols are redefined as follows: the symbol plus represents multiplication, the symbol minus represents addition, the symbol x represents division and the symbol ÷ represents subtraction. Using these coded meanings, evaluate the expression 50 + 3 ÷ 125 x 5 - 25 and find its correct value.

Introduction / Context:
This problem presents an expression where each arithmetic symbol has a new meaning. Instead of using the usual meanings of plus, minus, multiplication and division, we are asked to use a coded interpretation and then evaluate the expression accordingly. This tests the ability to handle symbolic substitutions carefully and to maintain correct order of operations. It is a common type of reasoning question in competitive examinations, designed to check attention to detail and comfort with basic arithmetic.

Given Data / Assumptions:

• The symbol + represents multiplication.
• The symbol - represents addition.
• The symbol x represents division.
• The symbol ÷ represents subtraction.
• The expression to evaluate is 50 + 3 ÷ 125 x 5 - 25.
• We must apply standard arithmetic precedence after translating the symbols to their true meanings.

Concept / Approach:
The key step is to translate the coded expression into a standard arithmetic one by replacing each symbol with its corresponding real operation. After substitution, we obtain a normal expression containing only the usual plus, minus, multiplication and division symbols. Then we can evaluate it using the usual rules: perform multiplication and division before addition. It is important not to rush into calculations without first completing a clear symbol replacement, because mixing the old and new meanings can easily cause mistakes.

Step-by-Step Solution:
Step 1: Start from the coded expression: 50 + 3 ÷ 125 x 5 - 25. Step 2: Replace each symbol using the given meanings. Here + becomes multiplication, ÷ becomes subtraction, x becomes division and - becomes addition. Step 3: After substitution, the expression becomes 50 * 3 - 125 / 5 + 25. Step 4: Apply arithmetic precedence. Compute multiplication and division first: 50 * 3 = 150 and 125 / 5 = 25. Step 5: Substitute these results back: the expression simplifies to 150 - 25 + 25. Step 6: Now perform the remaining operations from left to right: 150 - 25 = 125, then 125 + 25 = 150. Step 7: Therefore the value of the coded expression is 150.

Verification / Alternative check:
To verify our calculation, we can recompute more slowly or even bracket operations explicitly. Writing the substituted form as (50 * 3) - (125 / 5) + 25 makes the precedence clear. Evaluating those parts again gives 150, 25 and 25 respectively, and combining them yields 150. Since there is no ambiguity in the mapping of symbols and the arithmetic steps are straightforward, we can be confident that 150 is the correct result.

Why Other Options Are Wrong:
Option 31 or 17 would arise only if subtraction and addition were mishandled or if the division and multiplication were incorrectly ordered. Option 55 might come from partially correct steps but with a misapplied sign. Option 75 could appear if someone mistakenly divided 150 by 2 at the end or treated the minus as its original meaning. None of these values match the correct evaluation of the expression under the coded rules. Only 150 faithfully reflects all the required substitutions and precedence rules.

Common Pitfalls:
A very common mistake is to forget that + no longer means addition in the coded expression and to compute 50 + 3 as 53. Another frequent error is to ignore operator precedence and work strictly from left to right after substitution, which can change the result. Some learners also misremember which symbol maps to which operation. Writing down a small legend for the mapping and then fully rewriting the expression before doing any numeric work is a reliable way to avoid such errors.

Final Answer:
After substituting the coded meanings and evaluating with correct precedence, the value of 50 + 3 ÷ 125 x 5 - 25 is 150.