The real numbers x, y and z satisfy the equations x+2y+3z=950 and 3x+2y+z=450 . What is the average of x, y and z ?
If we add the equations given in the question, we get $4x+4y+4z = 1400. $ Dividing by $4$ on each side, we get $x+y+z=350.$ Therefore, the average of $x,y,z$ is just $\frac{x+y+z}{3} = \boxed{\frac{350}{3}}.$
