For this problem A is the amount of salt in the tank.
If a tank contains $175$ liters of liquid with $15$ grams of salt. A mixture containing $7$ grams per liter is pumped into the tank at a rate of $5$ liters/minute. The mixture is well-mixed, and pumped out at a rate of $8$ liters/minute. The amount of salt in the tank satisfies the differential equation
$= 0$.
Rewriting this as a linear differential equation we get
$= 35$
The integrating factor is and the solution is