A $400-$liter tank initial contains $100$ liters of water containing $2\mathrm{.}5$ kilograms of salt. Suppose that water containing $0\mathrm{.}2$ kilograms of salt per liter flows into the top of the tank at a rate of $10$ liters per minute. The tank is kept well mixed, and $8$ liters per minute are removed from the bottom of the tank. How much salt is in the tank when the tank is full? Round your answer to the nearest tenth of a kilogram.

Use $\backslash ($ x$($t$)\backslash )$ for the amount of salt $($in kilograms$)$ in the tank after $\backslash ($ t $\backslash )$ minutes, and you may assume that $\backslash (0\backslash$leq t $\backslash$leq $150\backslash )$ minutes.