This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The problem asks us to identify which two numbers should be interchanged in the given equation to make it mathematically correct. The equation is: 36 × 11 ÷ 3 - 10 + 4 = 49 First, let's calculate the current value of the left side of the equation using the order of operations (BODMAS/PEMDAS): 1. Multiplication and Division (from left to right): 36 × 11 = 396 396 ÷ 3 = 132 So the equation becomes: 132 - 10 + 4 2. Addition and Subtraction (from left to right): 132 - 10 = 122 122 + 4 = 126 Currently, the equation is 126 = 49, which is incorrect. We need to find an interchange of two numbers that makes the left side equal to 49. Let's test each option: Option 1: Interchange 10 and 4 The equation becomes: 36 × 11 ÷ 3 - 4 + 10 1. 36 × 11 = 396 2. 396 ÷ 3 = 132 3. 132 - 4 = 128 4. 128 + 10 = 138 Since 138 ≠ 49, this option is incorrect. Option 2: Interchange 4 and 11 The equation becomes: 36 × 4 ÷ 3 - 10 + 11 1. 36 × 4 = 144 2. 144 ÷ 3 = 48 3. 48 - 10 = 38 4. 38 + 11 = 49 Since 49 = 49, this option is correct. Let's quickly check the other options to confirm. Option 3: Interchange 49 and 36 This option suggests swapping the target value (49) with a number in the expression (36). If we interpret this as making the left side equal to 36, it would be: 49 × 11 ÷ 3 - 10 + 4 539 ÷ 3 - 10 + 4 This will not result in an integer, and certainly not 36. This option is incorrect. Option 4: Interchange 11 and 3 The equation becomes: 36 × 3 ÷ 11 - 10 + 4 1. 36 × 3 = 108 2. 108 ÷ 11 is not an integer (108/11 ≈ 9.81). This will not result in 49. This option is incorrect. Therefore, interchanging 4 and 11 makes the equation correct. The final answer is 2