Three numbers are given such that when the average of

Solution

ATQ,

Let the numbers be A, B, and C. Given: (A + B)/2 + C = 450 → A + B + 2C = 900 (B + C)/2 + A = 420 → B + C + 2A = 840 (C + A)/2 + B = 400 → C + A + 2B = 800 Add all three equations: A + B + 2C B + C + 2A C + A + 2B = 900 + 840 + 800 = 2540 4A + 4B + 4C = 2540 A + B + C = 635 From A + B + C = 635: Use A + B + 2C = 900 (635 - C) + 2C = 900 → C = 265 Use A + C + 2B = 800 (635 - B) + 2B = 800 → B = 165 A = 635 - B - C = 635 - 165 - 265 = 205 Final values: A = 205 B = 165 C = 265 Difference between largest and smallest: 265 - 165 = 100