Describe the plan that Petruchio and Hortensio develop to allow Hortensio to become close to Bianca.
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Petruchio explains that he is looking for a rich wife. Hortensio mentions Katharina, telling Petruchio that she is rich but a shrew; Petruchio however, isn't bothered by Hortensio's description - he is willing to wed anyone with enough money. Grumio interjects that, no matter how sharp-tongued Katharina may be, she could not match the rhetorical weaponry Petruchio has at his disposal.
Hortensio then asks Petruchio to present to Baptista, "disguised in sober robes" (1.2: 130), as a schoolmaster. At the same time, Lucentio appears disguised as the schoolmaster Cambio. Lucentio has convinced the old suitor, Gremio, that he will plead his case to Bianca. Hortensio states to Gremio that he too has found someone who will teach Bianca music, and adds that Petruchio is willing to wed Katharina.