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 find which two numbers, when interchanged in the given equation, will make the equation correct. The given equation is: 25 - 28 + 21 × 10 ÷ 5 = 43 First, let's evaluate the left-hand side (LHS) of the equation using the order of operations (BODMAS/PEMDAS): 25 - 28 + 21 × 10 ÷ 5 Step 1: Perform division. 10 ÷ 5 = 2 The equation becomes: 25 - 28 + 21 × 2 Step 2: Perform multiplication. 21 × 2 = 42 The equation becomes: 25 - 28 + 42 Step 3: Perform addition and subtraction from left to right. 25 - 28 = -3 -3 + 42 = 39 So, currently, the equation is 39 = 43, which is incorrect. We need to find a swap that makes the LHS equal to 43. Let's test each option: Option 1: Swap 5 and 28 The equation becomes: 25 - 5 + 21 × 10 ÷ 28 25 - 5 + 21 × (10)/(28) 20 + 21 × (5)/(14) 20 + (3 × 7 × 5)/(2 × 7) 20 + (15)/(2) = 20 + 7.5 = 27.5 Since 27.5 ≠ 43, this option is incorrect. Option 2: Swap 21 and 25 The equation becomes: 21 - 28 + 25 × 10 ÷ 5 Step 1: Perform division. 10 ÷ 5 = 2 The equation becomes: 21 - 28 + 25 × 2 Step 2: Perform multiplication. 25 × 2 = 50 The equation becomes: 21 - 28 + 50 Step 3: Perform addition and subtraction from left to right. 21 - 28 = -7 -7 + 50 = 43 Since 43 = 43, this option makes the equation correct. Option 3: Swap 10 and 43 The number 43 is the target value on the right-hand side of the equation, not a number within the expression to be swapped. Therefore, this option is not valid for this type of problem. Option 4: Swap 21 and 28 The equation becomes: 25 - 21 + 28 × 10 ÷ 5 Step 1: Perform division. 10 ÷ 5 = 2 The equation becomes: 25 - 21 + 28 × 2 Step 2: Perform multiplication. 28 × 2 = 56 The equation becomes: 25 - 21 + 56 Step 3: Perform addition and subtraction from left to right. 25 - 21 = 4 4 + 56 = 60 Since 60 ≠ 43, this option is incorrect. Based on the evaluation, swapping 21 and 25 makes the equation correct. The final answer is 21 এবং 25 Last free one today — make it count tomorrow, or type /upgrade for unlimited.