There are three numbers. If the average of any two of them is added to the third number, the sums obtained are 177, 163 and 138. Whatis the average of the largest and the smallest of the given numbers?

Given

There are three numbers if the average of any two of them is added to third number the sum obtained are 177, 163 and 138  

To find:

What is the average of the largest and the smallest of the given numbers

Solution:

Let the three numbers be x, y, z.

$$\frac{x+y}{2}$$+z=177

x + y + 2z = 354 …(1)

$$\frac{y+z}{2}$$+x = 163

2x + y + z = 326 …(2)

$$\frac{x+z}{2}$$+ y = 138

x + 2y + z = 276 …(3)

Adding eq(1),(2),(3) and dividing it by 4, we get

x + y + z = 239 ,,,(4)

sub  (1) - (4),  z = 115

sub (2) - (4),   x = 87

sub (3) - (4),   y = 37

The average of largest and smallest =

$$\frac{115+37}{2}$$=76