Answer
$y=573 $ at-bats.
Work Step by Step
Typical percentage problem:
What percent ($n$, as a decimal number) of (the base amount $y$) is $x?$
Translated:$\quad n\cdot y=x$
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Here, What percent ($n$, as a decimal number) of ($y=?$) is ($x=197$)$?$
Translated:$\quad 0.344\cdot y=197$
... divide with $0.344$
$y=573$