In a certain code language, the arithmetic symbols are redefined as follows: "+" represents multiplication, "-" represents addition, "x" represents division and "÷" represents subtraction. Using these coded operators, what is the value of 50 + 5 - 700 x 28?

Introduction:
This problem again challenges us with redefined arithmetic operators in a coded language. Familiar symbols +, -, x, and ÷ no longer carry their usual meanings. We must translate each symbol according to the given rule and then compute the value of 50 + 5 - 700 x 28 correctly with ordinary precedence. This blends careful reading with basic arithmetic skills.

Given Data / Assumptions:
The code language uses the following interpretations:
1) "+" stands for multiplication.
2) "-" stands for addition.
3) "x" stands for division.
4) "÷" stands for subtraction.
The expression to be evaluated is 50 + 5 - 700 x 28. Once decoded, we carry out the operations using the standard order: division and multiplication first, then addition and subtraction from left to right.

Concept / Approach:
We start by systematically replacing each coded symbol with its true operator. This gives a standard arithmetic expression. After that, we apply familiar rules of BODMAS or PEMDAS. The most frequent sources of error are forgetting to translate one symbol or unconsciously using its normal meaning rather than the new one.

Step-by-Step Solution:
Step 1: Convert 50 + 5 using the new meaning of "+", which is multiplication. So 50 + 5 becomes 50 * 5.Step 2: Convert "- 700" using the fact that "-" means addition. So "- 700" becomes + 700.Step 3: Convert "x 28" using the fact that "x" means division. So "x 28" becomes / 28.Step 4: The fully decoded expression is 50 * 5 + 700 / 28.Step 5: Apply precedence: evaluate the multiplication and division before the addition.Step 6: Compute 50 * 5 = 250.Step 7: Compute 700 / 28. Since 28 * 25 = 700, we have 700 / 28 = 25.Step 8: Now add the results: 250 + 25 = 275.Step 9: Therefore, the value of 50 + 5 - 700 x 28 in the coded system is 275.

Verification / Alternative check:
We can verbally re phrase the decoded expression as "50 multiplied by 5 plus 700 divided by 28". That clearly yields 250 plus 25, again giving 275. There are no hidden brackets or secondary rules that alter the order of operations, so this answer is secure.

Why Other Options Are Wrong:
The values 94, 100, 90, and 255 might result from treating one or more symbols with their original meanings or from performing the operations strictly left to right without precedence. None of these incorrect methods respects both the reassigned meanings and the standard evaluation rules.

Common Pitfalls:
Students sometimes forget to convert the minus sign in the middle and still treat it as subtraction. Others may convert correctly but then handle 50 * 5 + 700 / 28 as (50 * 5 + 700) / 28, which is not implied by the expression. Always decode first, then apply the usual step by step calculation rules.

Final Answer:
Using the coded meanings of the operators, the expression evaluates to 275.