To simplify the expression \( \frac{49r + 18k + 7r + 82k}{5} \), we first combine like terms in the numerator.
Combine the \( r \) terms: \[ 49r + 7r = 56r \]
Combine the \( k \) terms: \[ 18k + 82k = 100k \]
Now, the numerator can be rewritten as: \[ 56r + 100k \]
So, the whole expression becomes: \[ \frac{56r + 100k}{5} \]
Now, simplify this expression by dividing each term in the numerator by \( 5 \): \[ \frac{56r}{5} + \frac{100k}{5} = 11.2r + 20k \]
Thus, the simplified expression is: \[ 11.2r + 20k \]