the arithmetic mean of x,y and z is 6 while that of x,y,z,t,u,v and w is w. Calculate the arithmetic mean of t,u,v and w.
To find the arithmetic mean of t, u, v, and w, we first need to find the value of w.
We are given that the arithmetic mean of x, y, and z is 6, which means that the sum of x, y, and z is 3 times the mean, or 3 * 6 = 18.
Next, we are told that the arithmetic mean of x, y, z, t, u, v, and w is w itself. This implies that the sum of these seven numbers is 7 times w, or 7w.
We can set up an equation using the two pieces of information we have:
x + y + z = 18
x + y + z + t + u + v + w = 7w
Since the first equation gives us the value of x + y + z, we can substitute it into the second equation:
18 + t + u + v + w = 7w
Simplifying this equation, we get:
t + u + v = 6w - 18
So, the arithmetic mean of t, u, v, and w would be:
(t + u + v) / 3 = (6w - 18) / 3 = 2w - 6
Therefore, the arithmetic mean of t, u, v, and w is 2w - 6.