Question
Three numbers are given such that when the average of
any two numbers is added to the third number, the resulting sums are 190, 185, and 180. Determine the difference between the largest and smallest numbers.Solution
ATQ;
Let the three numbers be x, y, and z.
So, 2x+y+z=190×2=380
x+2y+z=185×2=370
x+y+2z=180×2=360
Thus,4×(x+y+z)=1110
x+y+z=277.5
Now,
x=380−277.5=102.5
y=370−277.5=92.5
z=360−277.5=82.5
Desired difference = 102.5−82.5=20
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