Final answer:
To find the 4-digit whole number, we can use algebraic equations based on the given conditions. Solving these equations will give us the values of the digits. In this case, the 4-digit whole number is 6970.
Step-by-step explanation:
To find the 4-digit whole number, we need to analyze the given conditions. Swapping the 2 right-most digits increases the number by 27, swapping the left ones decreases the number by 5400, and swapping the middle ones increases the number by 90. Let's denote the digits of the number as ABCD, where A is the leftmost digit and D is the rightmost digit.
From the first condition, we have the equation: (1000B + 100A + 10D + C) - (1000A + 100B + 10D + C) = 27. Simplifying this equation, we get: 900(B - A) = 27. Therefore, B - A = 3.
From the second condition, we have the equation: (1000D + 100C + 10B + A) - (1000A + 100C + 10B + D) = -5400. Simplifying this equation, we get: 900(D - A) = -5400. Therefore, D - A = -6.
From the third condition, we have the equation: (1000C + 100B + 10A + D) - (1000C + 100D + 10A + B) = 90. Simplifying this equation, we get: 90(B - D) = 90. Therefore, B - D = 1.
Using these three equations, we can solve for the values of A, B, C, and D. We find that A = 6, B = 9, C = 7, and D = 0. Therefore, the 4-digit whole number is 6970.