Essay C as Personal Statement
Essay C doesn't have to be as difficult as climbing a mountain. It does, however, require some hard work and outside-the-box thinking to put forward a compelling response.
A wiser man than me once said that college admissions prompts are merely an "invitation to write." I love this phrase because it switches the role of applicant and reviewer. Instead of trying to fit your ideas into their prompt, make the prompt your own! An invitation to write empowers the applicant to consider what they want to write rather than trying to guess what the reviewer wants to read. Write what you want.
Especially for vague or general prompts, molding the essay question to fit your ideas opens up a lot of possibilities. This goes not just for talking about some ticket, but these short but difficult "Why X university?" or "Tell us about an interest!" prompts.
In 2013, the Apply Texas essays changed. Most notably, they added an Essay C that asked students to talk about their academic and future goals and ambitions. It read like a graduate school personal statement. UT used this essay to determine whether a student "fit" into their major.
UT still considers "fit" as a major factor in their review process - they want to see a demonstrated interest, curiosity, and prior experiences that influence why you have chosen your desired area of study. Absent a personal statement prompt, how do you fit "fit" into your essays?
Use Essay C!
Essays A and B offer a lot of opportunities to talk about how you were raised, an obstacle you confronted and overcame, or an important aspect of your identity. You can certainly talk about your ambitions there, but Essay C is a valuable opportunity to tell UT-Austin why you deserve a space in your chosen major and the university overall.
Choose an experience that guides your interest in your chosen major, tell a compelling story, and elaborate!
Don't get so caught up on the "ticket" phrasing of the question. Again, consider the prompt as an invitation to write rather than a mandate on how that needs to be done. It may help to write your Essay C as if it was a personal statement and integrate the ticket aspect at the end. I have a client doing just that right now for his desired major of computer science.
Most importantly, just write! In the early phases, all writing is good writing. Don't try and write the perfect sentence or get caught up on the phrasing of a prompt. Write what you want to and fitting your response to the question can come later.