Answer
$10$ consecutive hits
Work Step by Step
The new number of hits is $35+x$ (add x to the numerator),
out of $140+x$ outings with the bat (add x to the denominator).
$\displaystyle \frac{35+x}{140+x}=0.30$
$\displaystyle \frac{35+x}{140+x}=\frac{3}{10}\qquad $... $/\times 10(140+x)$
$10(35+x)=3(140+x)$
$ 350+10x=420+3x\qquad$ ... add $-350-3x$
$7x=70$
$x=10$
