The circus is coming to town. Sue is selling tickets. The first day she sold 4 senior citizen tickets and 2 children's tickets for a total of $80.

The circus is coming to town. Sue is selling tickets. The first day she sold 4 senior citizen tickets and 2 children's tickets for a total of $80. The second day she received $145 for 5 senior citizen tickets and 7 children's tickets. What is the price of a child's ticket and a senior citizen ticket? 

 show how you solved the problem by using correct mathematical symbols and by explaining thoroughly in words each step.