In a certain code language for arithmetic, the symbol plus represents multiplication, minus represents addition, x represents division and the division sign ÷ represents subtraction. Using this code, what is the result of the expression 825 x 25 - 27 ÷ 10?

Introduction / Context:
This coding and decoding problem uses operator substitution in arithmetic expressions. Each common operator is given a new meaning. To solve the expression 825 x 25 - 27 ÷ 10, you must decode the operators into their real operations first and then evaluate the resulting standard arithmetic expression using the usual order of operations.

Given Data / Assumptions:

• The plus symbol (+) represents multiplication.
• The minus symbol (−) represents addition.
• The symbol x represents division.
• The division sign (÷) represents subtraction.
• The coded expression is 825 x 25 - 27 ÷ 10.
• After decoding, we use normal precedence: division and multiplication before addition and subtraction.

Concept / Approach:
The crucial step is to rewrite the coded expression in true arithmetic form by replacing each operator with what it actually stands for in the code language. Once that is done, we use standard arithmetic rules to simplify. This approach prevents the common error of trying to solve the expression directly with the visible symbols.

Step-by-Step Solution:
Step 1: Begin with the coded expression 825 x 25 - 27 ÷ 10.Step 2: Replace x with its real meaning, which is division. Thus 825 x 25 becomes 825 ÷ 25.Step 3: Replace the minus sign with its real meaning, which is addition. So the symbol between 25 and 27 becomes a plus, giving + 27.Step 4: Replace the division sign ÷ with its real meaning, which is subtraction. So ÷ 10 becomes − 10.Step 5: The fully decoded expression is 825 ÷ 25 + 27 − 10.Step 6: Now apply the order of operations. First compute the division: 825 ÷ 25.Step 7: Perform the division: 25 goes into 825 exactly 33 times, so 825 ÷ 25 = 33.Step 8: Substitute back to get 33 + 27 − 10.Step 9: Now do addition and subtraction from left to right. First 33 + 27 = 60.Step 10: Then 60 − 10 = 50.Step 11: Therefore, the value of the coded expression is 50.

Verification / Alternative check:
You can verify the calculation by recomputing 825 ÷ 25 using long division or breaking it into 25 × 33 = 825. Recalculating 33 + 27 − 10 again gives 50. Since all operator substitutions have been applied consistently and the arithmetic checks out, the answer 50 is confirmed.

Why Other Options Are Wrong:
The option 100 might come from misinterpreting x as multiplication and computing 825 × 25, which is completely different. The option 25 may occur if someone divides 825 by 33 or makes a slip in the final subtraction. The options 20 and 40 could arise from incorrect intermediate additions or subtractions. None of these values match the correctly decoded and evaluated expression.

Common Pitfalls:
Students frequently forget one of the substitutions, for example treating the minus sign as subtraction instead of addition. Another mistake is ignoring operator precedence and evaluating from left to right. A third pitfall is performing the division 825 ÷ 25 incorrectly. Carefully applying each substitution and then simplifying stepwise prevents these errors.

Final Answer:
After performing the correct substitutions and calculations, the value of 825 x 25 - 27 ÷ 10 is 50.