$(1$ point$)$ A tank is filled with $1000$ liters of pure water. Brine containing $0\mathrm{.}09$ kg of salt per liter enters the tank at $10$ liters per minute. Another brine solution containing $0\mathrm{.}09$ kg of salt per liter enters the tank at $9$ liters per minute. The contents of the tank are kept thoroughly mixed and the drains from the tank at $19$ liters per minute.

A$.$ Determine the differential equation which describes this system. Let S$($t$)$ denote the number of kg of salt in the tank after t minutes. Then

dSdt$=$

B$.$ Solve the differential equation for S$($t$).$

S$($t$)=$

$$ At least one of the answers above is NOT correct.

$(1$ point$)$ A tank is filled with $1000$ liters of pure water. Brine containing $0\mathrm{.}03$ kg of salt per liter enters the tank at $9$ liters per minute. Another brine solution containing $0\mathrm{.}09$ kg of salt per liter enters the tank at $10$ liters per minute. The contents of the tank are kept thoroughly mixed and the drains from the tank at $19$ liters per minute.

A$.$ Determine the differential equation which describes this system. Let $\backslash ($ S$($t$)\backslash )$ denote the number of kg of salt in the tank after $\backslash ($ t $\backslash )$ minutes. Then $\backslash (\backslash$frac$\{$d S$\}\{$d t$\}=\backslash )$

B$.$ Solve the differential equation for $\backslash ($ S$($t$)\backslash ).$

$\backslash [$

S$($t$)=$

$\backslash ]$