If the difference between the average of d and e and that of e and h is 19, what will be the difference between d and h?

Options

A. 38
B. 22
C. 9
D. 19

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Averages
We need to find the average of two pairs:
- The average of \( d \) and \( e \) is given by:
\[ \text{Average of } d \text{ and } e = \frac{d + e}{2} \]
- The average of \( e \) and \( h \) is given by:
\[ \text{Average of } e \text{ and } h = \frac{e + h}{2} \]

### Step 2: Set Up the Equation
According to the problem, the difference between these two averages is 19:
\[ \left(\frac{d + e}{2}\right) - \left(\frac{e + h}{2}\right) = 19 \]

### Step 3: Simplify the Equation
To simplify, we can eliminate the fractions by multiplying the entire equation by 2:
\[ (d + e) - (e + h) = 38 \]

### Step 4: Rearrange the Equation
Now, we can rearrange the equation:
\[ d + e - e - h = 38 \]
This simplifies to:
\[ d - h = 38 \]

### Step 5: Find the Difference Between \( d \) and \( h \)
From the rearranged equation, we can see that:
\[ d - h = 38 \]
Thus, the difference between \( d \) and \( h \) is 38.

### Final Answer
The difference between \( d \) and \( h \) is **38**.

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