If `2s-e=32 and 2e-d=10`, what is the average of d and e?

Answer

To solve the problem, we have the following two equations:

1. \( 2d - e = 32 \) (Equation 1)
2. \( 2e - d = 10 \) (Equation 2)

We need to find the average of \( d \) and \( e \), which is given by the formula:

\[ \text{Average} = \frac{d + e}{2} \]

### Step 1: Solve the equations simultaneously

Let's add the two equations together to eliminate one of the variables.

From Equation 1:
\[ 2d - e = 32 \]

From Equation 2:
\[ 2e - d = 10 \]

Adding these two equations:
\[ (2d - e) + (2e - d) = 32 + 10 \]

### Step 2: Simplify the left side

Combine like terms:
\[ 2d - d + 2e - e = 32 + 10 \]

This simplifies to:
\[ d + e = 42 \]

### Step 3: Find the average of \( d \) and \( e \)

Now that we have \( d + e = 42 \), we can find the average:
\[ \text{Average} = \frac{d + e}{2} = \frac{42}{2} = 21 \]

### Final Answer

The average of \( d \) and \( e \) is \( 21 \).

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