Like ふうに, the grammar point indicating that something is being done ‘in the way of (A)’, というふうに uses the same suffix of 風（ふう） ‘wind’, ‘air’, to express that something is being done ‘as if to say (A)’, ‘as if to suggest (A)’, or ‘in such a way that (A)’.
As this construction is just a combination of という ‘to say’, and ふうに ‘in a manner’, the literal meaning of this expression is similar to ‘in a way that would say that (A)’. This simply highlights the speaker's uncertainty about what the actual situation is, and that they are only commenting on appearances.
というふうに may be seen directly after verbs, or after nouns expressing the way in which something is being done. The (B) portion of these phrases will then indicate exactly what is being done ‘in a way as if to say (A)’.

• 彼女（かのじょ）は昼（ひる）休憩（きゅうけい）に帰（かえ）るというふうに聞（き）いています。
  I heard something as if to suggest that she is going to go home during lunch break.
• 鈴木（すずき）さんはこの試験（しけん）に命（いのち）がかかっているというふうに勉強（べんきょう）をした。
  Suzuki-san studied as if to suggest that his life depended on this exam.
• 私（わたし）は今（いま）まで自分（じぶん）が一番（いちばん）仕事（しごと）ができる人（ひと）だというふうに思（おも）っていた。
  Until recently, I always thought in such a way as to suggest that I was the most capable person when it comes to work.
• 彼（かれ）はデザイン、僕（ぼく）はプログラミング、というふうに役割（やくわり）を分（わ）けてアプリを開発（かいはつ）することにした。
  We decided to develop the application by dividing the roles in the following way: he would do the design and I would do the programming.