I'll be taking pre-calc soon, and I've been wondering about something.

I know that some problems can be solved with algebra.

Example:

Tickets for a school play are $12 for adults and $8 for students. The school sold 200 tickets for Friday night. If the school earned $1,860 for the show, how many $12 tickets did they sell.

I can solve this example writing

12x + 8y = 1860

x + y = 200

(Can solve by elimination or substitution)

So, I was wondering if anyone could give me an example of a problem that cannot be solved by using only Algebra and must us Calculus to solve it.