The arithmetic mean of x,y andz is 6 while that of x,y,z,t,u,v and w is 9. Calculate the arithmetic mean of t,u,v and w
Ok. I'll show some maybe-not-so-divine mercy and help you out.
(x+y+z)/3 = 6
(x+y+z+t+u+v+w)/7 = 9
x+y+z = 18
x+y+z+t+u+v+w = 63
18+t+u+v+w = 63
t+u+v+w = 45
(t+u+v+w)/4 = 45/4
To calculate the arithmetic mean, we need to sum up all the numbers and then divide by the total number of values.
Let's start by adding up the values for x, y, and z:
x + y + z = 6 * 3 = 18
Next, we have the mean of x, y, z, t, u, v, and w, which is 9.
We can express this as:
(x + y + z + t + u + v + w) / 7 = 9
Now, let's substitute the sum of x, y, and z (which we found earlier as 18) into the equation:
(18 + t + u + v + w) / 7 = 9
Multiply both sides of the equation by 7 to eliminate the denominator:
18 + t + u + v + w = 63
To calculate the mean of t, u, v, and w, we need to find their sum and then divide it by the total number of values, which is 4. We can write the equation as:
(t + u + v + w) / 4 = arithmetic mean
We want to find the value of the arithmetic mean, so let's isolate it:
(t + u + v + w) = arithmetic mean * 4
Now we can substitute the value of the sum from the previous equation:
18 + t + u + v + w = 63
Rearranging the equation to isolate the sum:
t + u + v + w = 63 - 18
Simplifying the right side of the equation:
t + u + v + w = 45
Substituting this sum back into the equation for the arithmetic mean:
(t + u + v + w) / 4 = arithmetic mean
(45) / 4 = arithmetic mean
Therefore, the arithmetic mean of t, u, v, and w is 45/4, which is 11.25.