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Gradgrind realizes that Louisa and Tom are growing up; this means that it is time for Tom to go work at Bounderby's Bank.
Sissy and Gradgrind discuss her scholastic failures. Gradgrind acknowledges that she works as hard as she can to learn the facts, figures, and exact knowledge, but is just not cut out to be taught according to his system. And she has some qualities that are just going to have to be enough: she is "affectionate, earnest, good."
Sometime later, Gradgrind is elected a Member of Parliament.
He notices that Louisa is now finally a woman. He asks her to come to his study to discuss something serious the next day.
That night, Tom stops by the house. He tells Loo that Gradgrind and Bounderby are meeting at the Bank, most likely to discuss Bounderby wanting to marry Louisa.
Her brother then proceeds to lay an extremely selfish and ridiculous guilt trip on her, basically telling her that if she loves him, she will go marry Bounderby. Because that way she can help Tom be even more of a scuzz than he has already become. Sadly, she really has no one else to love, so she agrees to keep Tom in mind when making her decision.