Understanding the Equation Problem

The question asks us to find the value of the expression [(48 - 2)  ÷  23]  ×  19 + 3 after interchanging specific mathematical operators. We need to replace the subtraction ('-') with division ('÷') and division ('÷') with subtraction ('-'). Similarly, we must replace multiplication ('×') with addition ('+') and addition ('+') with multiplication ('×').

Applying Operator Interchanges

Let's look at the original equation:

[(48 - 2)  ÷  23]  ×  19 + 3

The given interchanges are:

• '-' is interchanged with '÷'
• '×' is interchanged with '+'

Applying these rules to the original equation:

• The '-' inside the bracket becomes '÷'.
• The '÷' outside the bracket becomes '-'.
• The '×' becomes '+'.
• The '+' becomes '×'.

The equation after interchanging the symbols becomes:

[(48  ÷  2) - 23] + 19  ×  3

Step-by-Step Calculation

Now, we solve the new equation using the standard order of operations (BODMAS/PEMDAS): Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

1. Solve the expression inside the innermost part of the bracket: First, perform the division within the parentheses: (48  ÷  2) Using LaTeX notation: \( 48 \div 2 = 24 \)
2. Continue with the expression inside the main bracket: Now substitute the result back into the bracket: [24 - 23] Perform the subtraction: 24 - 23 = 1 Using LaTeX notation: \( 24 - 23 = 1 \)
3. Rewrite the equation with the bracket value: The equation now simplifies to: 1 + 19  ×  3 Using LaTeX notation: \( 1 + 19 \times 3 \)
4. Perform the multiplication: According to the order of operations, multiplication comes before addition. 19  ×  3 Using LaTeX notation: \( 19 \times 3 = 57 \)
5. Perform the final addition: Substitute the multiplication result back into the equation: 1 + 57 Perform the addition: 1 + 57 = 58 Using LaTeX notation: \( 1 + 57 = 58 \)

Therefore, the value that comes in place of the question mark (?) is 58.