Question

Three different numbers are chosen such that when the average of the any two numbers is added to the third number, it gives 65, 69 and 76 as result. The average of the three numbers is

Answer 1

65+69+76=210

Answer 2

210/3=70,70/2=35

Answer 3

Let the numbers be x, y and z.
Average of x and y + z = 65
i.e \(\frac{x+y}{2} + z = 65\) eqn (1)
Similarly for other numbers
\(\frac{y+z}{2} + x = 69\) eqn (2)
and
\(\frac{z+x}{2} + y = 76\) eqn (3)

Add eqns (1),(2) and (3) to get
2(x+y+z) =210
x+y+z =105
Average of the three numbers is \(\frac{x+y+z}{3} = \frac{105}{3} = 35\)

Answer 4

my answer is correct 35?

Answer 5

Yes

Answer 6

Yes.
Refer to the attachment from Mathematica.