It is given that

$$ Cost\ of\ cake=\$35 $$

$$ Catering\ expenses\ per\ person=\$15 $$

Then

$$ Total\ Cost=\$35+\$15p $$

As they will spend at most $\$300$ for his party, the total cost should be less than or equal to $\$300$.

$$ \therefore \$35+\$15p\leq 300 $$

So choice K is correct.