Our school's art teacher took his class to a concert hall and paid $512 for 10 adult
tickets and 9 children tickets. The next day, our music teacher took our class to the
same concert hall and paid a total of $831 dollars for 17 children and 15 adults.
If a represents the price of an adult ticket, and c represents the price of a child's ticket,
which system of equations can be used to find how much each child ticket and each
adult ticket cost?