A chemist is mixing two solutions, Solution A and Solution B, each containing a certain concentration of solute in grams per liter. Solution A has a concentration of $A$ grams per liter, and Solution B has a concentration of $B$ grams per liter.

When 5 liters of Solution A are mixed with 3 liters of Solution B, the total amount of solute is 400 grams. When 2 liters of Solution A are mixed with 7 liters of Solution B, the total amount of solute is 450 grams.

What is the concentration, in grams per liter, of Solution A?