Solving Expression with Symbol Substitution

The question asks us to find the value of a given expression where letters represent arithmetic operators. We need to substitute the letters with their corresponding operators and then evaluate the resulting mathematical expression following the correct order of operations.

The given substitutions are:

• 'A' means '+' (Addition)
• 'B' means '-' (Subtraction)
• 'C' means '×' (Multiplication)
• 'D' means '÷' (Division)

The expression is given as: $25 \text{ Vcy } 35 \text{ A } 12 \text{ C } 25 \text{ D } 5 = ?$

Looking at the provided mapping, it seems 'Vcy' in the expression is likely a typo and should correspond to one of the given operators. Given the operator 'B' means '-', it is reasonable to assume 'Vcy' is intended to be 'B'. Let's proceed with this assumption.

Substituting the letters with the operators based on the assumption ('Vcy' means '-'):

The expression becomes: $25 - 35 + 12 \times 25 \div 5$

Evaluating the Expression using BODMAS

To evaluate the expression $25 - 35 + 12 \times 25 \div 5$, we must follow the order of operations, often remembered by the acronym BODMAS or PEMDAS.

• Brackets / Parentheses
• Orders / Exponents
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Let's evaluate the expression step-by-step:

1. Division: Perform the division operation first. $$12 \times 25 \div 5$$ $$12 \times (25 \div 5)$$ $$12 \times 5$$ The expression is now: $25 - 35 + 12 \times 5$
2. Multiplication: Perform the multiplication operation. $$12 \times 5 = 60$$ The expression is now: $25 - 35 + 60$
3. Addition and Subtraction: Perform addition and subtraction from left to right. First, subtraction: $$25 - 35 = -10$$ The expression is now: $-10 + 60$ Next, addition: $$-10 + 60 = 50$$

So, the value of the expression $25 \text{ Vcy } 35 \text{ A } 12 \text{ C } 25 \text{ D } 5$, assuming 'Vcy' is 'B', is 50.

Checking the Options

Let's compare our result with the given options:

• Option 1: 45
• Option 2: 50
• Option 3: 55
• Option 4: 40

Our calculated value, 50, matches Option 2.

Revision Table: Operator Substitution & BODMAS

BODMAS/PEMDAS Order:

Additional Information on Order of Operations

The order of operations is crucial in mathematics to ensure that everyone gets the same result when evaluating an expression. Without a standard order, an expression like $2 + 3 \times 4$ could be interpreted in two ways: $(2 + 3) \times 4 = 5 \times 4 = 20$ or $2 + (3 \times 4) = 2 + 12 = 14$. The BODMAS/PEMDAS rule resolves this ambiguity, stating that multiplication should be done before addition, giving the result 14.

In the case of division and multiplication, or addition and subtraction, the operations are performed from left to right. For example, in $10 \div 2 \times 5$, division is done first ($10 \div 2 = 5$), then multiplication ($5 \times 5 = 25$). If we did multiplication first ($2 \times 5 = 10$), then division ($10 \div 10 = 1$), the result would be different and incorrect according to the standard rule.