How does Jem solve Scout's problem with Walter Cunningham in chapter 3 of To Kill a Mockingbird?
In chapter 2, Scout tried to help her teacher Miss Caroline understand how the Cunninghams function in Maycomb society. She wasn't received well because she also had another strike against her--she already knew how to read. As a result, Miss Caroline struck Scout's knuckles and the class laughed at her. To pay Walter back for the humiliation, she decided to rough him up a bit at lunch time. Jem walked up and complained that Scout beating up on Walter wasn't fair because she was bigger than he was. Scout claimed that didn't matter because Walter was older than she. In an effort to save Walter from his sister's wrath, Jem invites him home for lunch. He first asks if Walter's father is from Old Sarum. Walter stood there a little bewildered with what was going on until Jem did the following:
"Jem suddenly grinned at him. 'Come on home to dinner with us, Walter,' he said. 'We'd be glad to have you.' Walter's face brightened, then darkened. Jem said, 'Our daddy's a friend of your daddy's. Scout here, she's crazy--she won't fight you any more" (23).
Fortunately, Scout follows her brother's lead and promises not to beat up Walter. She even asks him if she likes butter beans. For a very stubborn, but hungry Cunningham, that sounded good enough. He waited until Scout and Jem got to the Radley's house before he decided to join them. Therefore, Jem solves the problem between Scout and Walter by being a good example for his sister, and doing a kind deed by asking Walter over for dinner.
Scout was busy rubbing Walter Cunningham Jr.'s nose in the playground dirt as payback for the trouble he had caused her with Miss Caroline when Jem came by. Jem got his sister to stop fighting with Walter, coming up with a friendlier plan: They would invite him home for lunch instead. Scout finally cooled off, and Atticus welcomed Walter, talking "together like two men." Walter obviously got very little to eat at his own home, because he "piled food on his plate" once Calpurnia had served it. Scout also got a lesson on hospitality from Cal after making fun of Walter's habit of drencing all of his food in molasses, and Scout was soon able to call Walter her friend.