The average of w, x, y, and z is 31. If the average of w and y is 24, what is the average of x and z?

Answer

To solve the problem step by step, we will use the information given about the averages of the variables.

### Step 1: Understand the average of w, x, y, and z
The average of w, x, y, and z is given as 31. The formula for the average is:
\[ \text{Average} = \frac{w + x + y + z}{4} \]
Setting this equal to 31, we can write:
\[ \frac{w + x + y + z}{4} = 31 \]
Multiplying both sides by 4 gives:
\[ w + x + y + z = 31 \times 4 = 124 \]

### Step 2: Understand the average of w and y
We are also given that the average of w and y is 24. Using the average formula again:
\[ \frac{w + y}{2} = 24 \]
Multiplying both sides by 2 gives:
\[ w + y = 24 \times 2 = 48 \]

### Step 3: Substitute w + y into the equation for w + x + y + z
Now we know:
1. \( w + x + y + z = 124 \)
2. \( w + y = 48 \)

We can substitute \( w + y \) into the first equation:
\[ 48 + x + z = 124 \]

### Step 4: Solve for x + z
Now, we can isolate \( x + z \):
\[ x + z = 124 - 48 = 76 \]

### Step 5: Find the average of x and z
To find the average of x and z, we use the formula for average:
\[ \text{Average of } x \text{ and } z = \frac{x + z}{2} = \frac{76}{2} = 38 \]

Thus, the average of x and z is **38**.