At the Sunnyvale Play House, the price for an adult ticket is $12 and the price of a child's ticket is $6. For Saturday night's play, 125 tickets were sold, totaling $1,140. Which system of equations correctly represents this situation where a represents the number of adult tickets sold for Saturday night's play and c represents the number of child tickets sold?
1. a + c= 125 and 12a+6c=1140