the mean of x and y is 12 and the mean of y and 12 is z/2. what is the mean of x and z?
x + y = 24
y + 12 = z
x + y + 12 = 36
x + z = 36
(x + z) / 2 = 18
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To find the mean of x and z, we need to determine the values of x, y, and z.
Given information:
1. The mean of x and y is 12. This can be written as (x + y) / 2 = 12.
2. The mean of y and 12 is z/2. This can be written as (y + 12) / 2 = z/2.
Let's solve these equations step by step.
1. From the first equation, we have (x + y) / 2 = 12.
Multiplying both sides of the equation by 2, we get x + y = 24.
2. From the second equation, we have (y + 12) / 2 = z/2.
Multiplying both sides of the equation by 2, we get y + 12 = z.
3. Now, we have two equations:
x + y = 24 (Equation 1)
y + 12 = z (Equation 2)
To find the mean of x and z, we need to find their sum and divide by 2.
4. Adding Equation 1 and Equation 2, we get:
(x + y) + (y + 12) = 24 + z
Simplifying the equation, we have:
x + 2y + 12 = 24 + z
5. Rearranging the equation, we get:
x + z = 24 - 12 + 2y
x + z = 12 + 2y
Therefore, the mean of x and z is 12 + 2y.
To find the mean of x and z, we need to use the information given.
Let's break it down step by step:
1. We are given that the mean of x and y is 12, which means (x + y)/2 = 12. Rearranging the equation, we have x + y = 24.
2. We are also given that the mean of y and 12 is z/2. This means (y + 12)/2 = z/2. Cross multiplying, we have y + 12 = z.
Now we have two equations:
x + y = 24 ---> Equation 1
y + 12 = z ---> Equation 2
3. To find the mean of x and z, we need to find the sum of x and z, and then divide it by 2.
To get z, we will substitute the value of y from Equation 1 into Equation 2:
x + (24 - x) + 12 = z
36 = z
So, z = 36.
Now, we can find the mean of x and z:
Mean of x and z = (x + z)/2
= (x + 36)/2
Therefore, the mean of x and z is (x + 36)/2.