Which two numbers (not digits) should be interchanged to make the equation 72 – 6 + (18 ÷ 4) + 17 – (22 × 2) = 44 correct?

Question

Accepted Answer

Let's analyze the equation: 72 – 6 + (18 ÷ 4) + 17 – (22 × 2) = 44

First, calculate the original value:
1. 18 ÷ 4 = 4.5
2. 22 × 2 = 44
So, 72 – 6 + 4.5 + 17 – 44
= (72 – 6) + (4.5 + 17) – 44
= 66 + 21.5 – 44
= 87.5 – 44
= 43.5 (which is not 44)

Now, let's check each option by interchanging the numbers:

Option 1: Interchange 2 and 4
- Replace every 2 with 4 and every 4 with 2:
Equation: 72 – 6 + (18 ÷ 2) + 17 – (44 × 2)
18 ÷ 2 = 9
44 × 2 = 88
72 – 6 + 9 + 17 – 88 = 66 + 26 – 88 = 92 – 88 = 4 (Not 44)

Option 2: Interchange 22 and 18
Equation: 72 – 6 + (22 ÷ 4) + 17 – (18 × 2)
22 ÷ 4 = 5.5
18 × 2 = 36
72 – 6 + 5.5 + 17 – 36 = 66 + 22.5 – 36 = 88.5 – 36 = 52.5 (Not 44)

Option 3: Interchange 6 and 22
Equation: 72 – 22 + (18 ÷ 4) + 17 – (6 × 2)
18 ÷ 4 = 4.5
6 × 2 = 12
72 – 22 = 50
50 + 4.5 + 17 – 12 = 54.5 + 17 – 12 = 71.5 – 12 = 59.5 (Wait, let's check the placement:)
Original: 72 – 6 + (18 ÷ 4) + 17 – (22 × 2)
After interchange: 72 – 22 + (18 ÷ 4) + 17 – (6 × 2)
So, 72 – 22 = 50
18 ÷ 4 = 4.5
6 × 2 = 12
So, 50 + 4.5 + 17 – 12 = 54.5 + 17 – 12 = 71.5 – 12 = 59.5
Wait, this is not 44. Let's check if we made a calculation error.

Alternatively, let's try swapping the numbers in the brackets as well:
After swapping 6 and 22:
- 72 – 22 + (18 ÷ 4) + 17 – (6 × 2)
- 72 – 22 = 50
- 18 ÷ 4 = 4.5
- 6 × 2 = 12
- 50 + 4.5 = 54.5
- 54.5 + 17 = 71.5
- 71.5 – 12 = 59.5
Still not 44.

Let's try option 4: Interchange 6 and 4
Equation: 72 – 4 + (18 ÷ 6) + 17 – (22 × 2)
18 ÷ 6 = 3
22 × 2 = 44
72 – 4 = 68
68 + 3 + 17 – 44 = 71 + 17 – 44 = 88 – 44 = 44
This matches the required result!

So, the correct answer is option 4: 6 and 4.

Correction: The correct answer is option 4, not option 3.

Final answer:
Option 4: 6 and 4.

Answer

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