Tickets for a concert are sold at three prices: full, concessional and children.

Two full plus four concessional tickets cost $510, while four full, two concessional and seven children tickets cost $815.
Set up a system of equations. Find the general solutions and write your solutions on a piece of paper.
Now, we also know that the cost of a children ticket is one-third of the full cost, find the exact solution to the system of equations.