Reiko no Fuugi: Akuyaku Reijou to Yobarete Imasu ga, tada no Binbou Musume Desu

With the only thing she inherited from her parents being their once-great family name, the poverty-stricken Reiko Kujouin jumped at the chance to gain a scholarship to Meisei Private Academy, a prestigious high school for the wealthy. Why? Because of the ¥50,000 per month allowance and having all her school supplies being paid for, of course! But little could she expect that, on her very first day of classes, she would be tackled from behind by another girl who, convinced that she's been reincarnated into the world of an otome game, accuses Reiko of being a wealthy villainess...! Source: MU