In a coded arithmetic expression, the symbols P, Q, R, and S are used in place of ordinary operators as follows: P denotes addition (+), Q denotes subtraction (-), R denotes division (÷), and S denotes multiplication (x). Using this code, evaluate the expression 18 S 36 R 12 Q 6 P 7.

Introduction / Context:
This problem uses letter symbols to stand for basic arithmetic operations. Instead of directly reading plus, minus, multiplication and division, you must first translate the coded letters P, Q, R, and S into their respective operations. After decoding, the expression can be evaluated using normal arithmetic rules with correct precedence. This kind of question tests precision in substitution and understanding of the order of operations.

Given Data / Assumptions:

• P denotes + (addition). • Q denotes - (subtraction). • R denotes ÷ (division). • S denotes x (multiplication). • Expression: 18 S 36 R 12 Q 6 P 7.

Concept / Approach:
First convert the coded expression into an ordinary arithmetic expression by replacing each letter with its corresponding operator. Then compute the value step by step, remembering that multiplication and division must be performed before addition and subtraction. This systematic decoding and evaluation ensures that you do not mix the symbolic and actual meanings during calculation.

Step-by-Step Solution:
Step 1: Start with 18 S 36 R 12 Q 6 P 7. Step 2: Replace S with multiplication: 18 x 36. Step 3: Replace R with division: ÷ 12. Step 4: Replace Q with subtraction: − 6. Step 5: Replace P with addition: + 7. Step 6: The decoded expression is 18 x 36 ÷ 12 − 6 + 7. Step 7: Apply precedence, performing multiplication and division from left to right. First, 18 x 36 = 648. Step 8: Then 648 ÷ 12 = 54. Step 9: Now handle addition and subtraction: 54 − 6 + 7. Step 10: Compute 54 − 6 = 48. Step 11: Then 48 + 7 = 55.

Verification / Alternative check:
To verify, repeat the arithmetic quickly: 18 x 36 = 648, 648 ÷ 12 = 54, and 54 − 6 + 7 = 48 + 7 = 55. There is no ambiguity once the operators are decoded. The size of the numbers also makes sense; the multiplication followed by division brings the value back to a moderate range, and the final subtraction and addition adjust it slightly, yielding 55.

Why Other Options Are Wrong:
Option 115 is too large and would require a different sequence of operations or misinterpretation of the division. Option 65 might result from partial miscalculation after the division step. Option 25 is far from the correct value and indicates a more serious arithmetic or decoding error. Option 75 also does not correspond to any reasonable reworking of the decoded expression.

Common Pitfalls:
A common mistake is to evaluate 18 x 36 ÷ 12 as 18 x (36 ÷ 12) = 18 x 3 = 54, which, although numerically the same in this particular case, can cause confusion in other expressions. The safest habit is to move strictly from left to right for operators of the same precedence. Another pitfall is to forget to translate one of the coded symbols, especially near the end of the expression.

Final Answer:
After decoding and evaluating the expression, the correct value of 18 S 36 R 12 Q 6 P 7 is 55.