Chapter P, Prerequisites - Section P.9 - Modeling with Equations - P.9 Exercises - Page 71: 34

$714$ runs.

Let the amount of home runs Babe Ruth hit during his career be $x$. Therefore Hank Aaron hit $x+41$ runs. In total, they hit $(x)+(x+41)$ runs, which the problem stated was $1469$ runs. Set up the equation of $2x+41=1469$ and solve for $x=\frac{(1469-41)}{2}=714$ runs.