In a coded arithmetic system, the symbols represent operations as follows: "$" means addition, "@" means division, "#" means multiplication and "%" means subtraction. Using this code, what is the value of 84 @ 12 # 3 $ 24 % 35 ?

Introduction / Context:
This question uses special symbols to stand for the four basic arithmetic operations. The expression 84 @ 12 # 3 $ 24 % 35 must be translated from the symbolic language into a normal arithmetic expression and then evaluated. The primary skills tested are remembering the operator mappings correctly and applying the correct order of operations once translation is done.

Given Data / Assumptions:

• "$" means addition (+).
• "@" means division (÷).
• "#" means multiplication (×).
• "%" means subtraction (-).
• Coded expression: 84 @ 12 # 3 $ 24 % 35.
• Standard arithmetic precedence (× and ÷ before + and -) is applied after substitution.

Concept / Approach:
To solve the problem, we first convert each symbol into its corresponding arithmetic operator. This yields an ordinary expression involving division, multiplication, addition and subtraction. Then we evaluate the expression by performing division and multiplication from left to right before handling addition and subtraction. Carefully following these steps ensures that the calculation is accurate and consistent with standard mathematical rules.

Step-by-Step Solution:
Step 1: Translate each symbol. "@" is division, "#" is multiplication, "$" is addition and "%" is subtraction. Step 2: Replace the coded expression: 84 @ 12 # 3 $ 24 % 35 becomes 84 ÷ 12 × 3 + 24 - 35. Step 3: Apply precedence. First calculate 84 ÷ 12 = 7. Step 4: Then multiply 7 × 3 = 21. Step 5: Substitute this back into the expression to get 21 + 24 - 35. Step 6: Now perform addition and subtraction from left to right. First 21 + 24 = 45. Step 7: Then 45 - 35 = 10. Step 8: Therefore, the value of the coded expression is 10.

Verification / Alternative check:
We can quickly verify by bracketing the higher precedence operations: (84 ÷ 12 × 3) + 24 - 35. Evaluating inside the bracket gives 7 × 3 = 21, and the rest of the calculation proceeds exactly as before, resulting in 10. Because the mapping of symbols to operations is straightforward and consistently applied, there is no ambiguity, and 10 is clearly the correct result.

Why Other Options Are Wrong:
Options 9, 8, 6 and 12 are typical of arithmetic mistakes or precedence errors. For example, treating the operations from left to right without giving priority to division and multiplication can shift intermediate results, leading to incorrect final values. Similarly, misreading "%" as a modulus operator rather than subtraction could give different wrong answers. None of these values match the carefully computed result of 10 after correct translation and evaluation.

Common Pitfalls:
A common error is to misremember which symbol stands for which operation, particularly confusing "$" and "%", or "#" and "@". Another frequent mistake is to ignore operator precedence and evaluate the expression strictly in reading order. Writing the fully translated expression and underlining the division and multiplication parts before calculation helps reduce these mistakes. Always double check the mapping of each symbol to its true operation before starting the arithmetic.

Final Answer:
After decoding the symbols and computing correctly, the value of 84 @ 12 # 3 $ 24 % 35 is 10.