Applied integration? Dosage problem:

Hi all (Hi)

I'm a little rusty on my calculus and was wondering if I can get a little help. The problem involves linear dosing a Ca solution into an aquarium to increase the total concentration. Here are the numbers:

initial concentration: 360ppm

uptake: 2.5ppm per day

dosing adds: 7.5ppm per day

target concentration: 410ppm

So in words, the tank starts at 360ppm and I would like to get the concentration to 410ppm. Only one dose is allowed per day which adds 7.5ppm to the total concentration, but the uptake of the system consumes 2.5ppm per day. How many days/doses are needed to get 410ppm?

This is the instantaneous equation I came up with:

[(Target Ca conc - Ca conc + Ca consumed)] /[dosage amt] = #times you have to dose