This is a simplified version of a Baba Yaga story...
In this slightly sinister tale an evil witch (never referred to as Baba Yaga, but by her hut on chicken feet we know who she is!) has iron teeth and likes to eat children. When Sasha is sent to borrow a needle and thread she doesn't know what danger she is walking into. Luckily Sasha is a kind girl, and shares her butter, meat, and bread with a squeaky gate, a barking dog, and starving cat. They in turn are able to help her when she needs to escape.
Joanna Cole
Pictures by Dirk Zimmer 1983
(If Zimmer's pictures look familiar it's because he also illustrated that 80's classic "In a Dark, Dark Room")