Decoding the Coded Expression

The problem asks us to evaluate a mathematical expression where the standard arithmetic operators (+, -, ×, ÷) are replaced by letters ('a', 'b', 'c', 'd'). We need to substitute these letters with their corresponding operations and then solve the expression following the correct order of operations.

Operator Substitution

First, let's list the given substitutions:

• 'a' represents '+' (addition)
• 'b' represents '-' (subtraction)
• 'c' represents 'x' (multiplication)
• 'd' represents '÷' (division)

Applying Substitutions to the Expression

The expression given is $6a7b8c8d2a50$. Let's substitute the letters with their corresponding operators:

Replacing 'a' with '+', 'b' with '-', 'c' with 'x', and 'd' with '÷', the expression becomes:

$$6 + 7 - 8 \times 8 \div 2 + 50$$

Step-by-Step Calculation using BODMAS/PEMDAS

To solve this expression correctly, we must follow the order of operations (BODMAS/PEMDAS): Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

1. Division: Perform the division operation first ($8 \div 2$). $$8 \div 2 = 4$$ The expression now is: $$6 + 7 - 8 \times 4 + 50$$
2. Multiplication: Next, perform the multiplication operation ($8 \times 4$). $$8 \times 4 = 32$$ The expression becomes: $$6 + 7 - 32 + 50$$
3. Addition and Subtraction (Left to Right): Now, perform addition and subtraction from left to right.
   • First addition: $6 + 7 = 13$. The expression is now: $$13 - 32 + 50$$
   • Subtraction: $13 - 32 = -19$. The expression is now: $$-19 + 50$$
   • Final addition: $-19 + 50 = 31$.

Final Result

After performing all the operations in the correct order, the value of the expression $6a7b8c8d2a50$ is 31.