This question requires us to solve a mathematical expression where specific letters represent arithmetic operations. We need to substitute the given letters with their corresponding operators and then evaluate the expression following the standard order of operations (often remembered by the acronym BODMAS or PEMDAS).

Symbol Replacement in the Equation

First, let's identify the given expression and the rules for symbol replacement:

• The original expression is: 15A22B42C21D27
• The replacement rules are:
  • 'A' is replaced by '+'
  • 'B' is replaced by '-'
  • 'C' is replaced by ' ÷ '
  • 'D' is replaced by '×'

Applying these replacements to the expression, we get:

15 + 22 - 42 ÷ 21 × 27

Using mathematical notation, the expression is:

\(15 + 22 - 42 \div 21 \times 27\)

Evaluating the Equation Using BODMAS Rule

The BODMAS rule dictates the order in which operations should be performed:

1. Brackets
2. Orders (powers and square roots, etc.)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

Let's apply this rule step-by-step to our expression: \(15 + 22 - 42 \div 21 \times 27\)

Step 1: Applying Division Operation

According to BODMAS, division comes before multiplication, addition, and subtraction. We perform the division first:

\(42 \div 21 = 2\)

Substituting this back into the expression:

\(15 + 22 - 2 \times 27\)

Step 2: Applying Multiplication Operation

Next, we perform the multiplication:

\(2 \times 27 = 54\)

The expression now becomes:

\(15 + 22 - 54\)

Step 3: Performing Addition Operation

Now, we perform addition (working from left to right):

\(15 + 22 = 37\)

The expression simplifies to:

\(37 - 54\)

Step 4: Performing Subtraction Operation

Finally, we perform the subtraction:

\(37 - 54 = -17\)

Final Result of the Equation

After substituting the symbols and following the order of operations (BODMAS/PEMDAS), the value of the expression 15A22B42C21D27 is -17.