Math Puzzle: Understanding Operator Substitution

This problem presents a mathematical puzzle where standard arithmetic operators have been assigned new meanings. We need to decipher these substitutions and apply them to solve the given expression.

Decoding the Operator Substitution Rules

The question provides the following rules for substitution:

• $+= *$: This implies the addition operator $+$ should be replaced by the multiplication operator $*$.
• $- +$: This implies the subtraction operator $-$ should be replaced by the addition operator $+$.
• $= -$: This rule, along with the need to find a match among the options, suggests that the multiplication operator $*$, which appears in the expression, is replaced by the subtraction operator $-$.
• $/= /$: This implies the division operator $/$ remains unchanged.

Summarizing the derived operator mapping:

• $+$ becomes $*$
• $-$ becomes $+$
• $*$ becomes $-$
• $/$ remains $/$

Applying the Substitution to the Expression

The original expression is:

$(3 + 4) * 2 - 1 / 5$

Now, we substitute the operators according to our derived mapping:

• The $+$ inside the parentheses is replaced by $*$.
• The $*$ before $2$ is replaced by $-$.
• The $-$ before $1$ is replaced by $+$.
• The $/$ before $5$ remains $/$.

The transformed expression becomes:

$(3 \times 4) - 2 + \frac{1}{5}$

Step-by-Step Calculation Using BODMAS

We will now evaluate the transformed expression $(3 \times 4) - 2 + \frac{1}{5}$ using the standard order of operations (BODMAS/PEMDAS): Brackets, Orders, Division/Multiplication (from left to right), Addition/Subtraction (from left to right).

1. Brackets: Evaluate the expression inside the parentheses first. $(3 \times 4) = 12$
2. The expression is now: $12 - 2 + \frac{1}{5}$
3. Division: Perform the division next. $\frac{1}{5} = 0.2$
4. The expression is now: $12 - 2 + 0.2$
5. Subtraction and Addition (from left to right): Perform subtraction first as it appears before addition from the left. $12 - 2 = 10$
6. The expression is now: $10 + 0.2$
7. Addition: Finally, perform the addition. $10 + 0.2 = 10.2$

Final Result

Following the operator substitutions and the order of operations, the value of the expression $(3 + 4) * 2 - 1 / 5$ is 10.2.