John has a 25-gallon fish tank. John filled his tank today with 23-gallons of water. The water evaporates at a rate of 1.5 gallons per week. John adds 2 gallons to the tank every other week. At what following time will the tank contain 16.5 gallons?

To determine the time when the tank will contain 16.5 gallons, we need to calculate the amount of water remaining in the tank after a certain number of weeks.

First, let's calculate how much water evaporates from the tank each week. We know that the water evaporates at a rate of 1.5 gallons per week. Therefore, after n weeks, the amount of water that has evaporated from the tank would be 1.5 * n gallons.

Next, we need to determine how much water John adds every other week. Since he adds 2 gallons to the tank every other week, after n weeks, he would have added 2 * (n / 2) gallons to the tank.

Now, let's calculate the net change in the water level. The initial amount of water in the tank is 23 gallons, but we subtract the amount that has evaporated and add the amount that John has added. Therefore, after n weeks, the net change in the water level would be 23 - (1.5 * n) + (2 * (n / 2)) gallons.

To find the number of weeks when the tank will contain 16.5 gallons, we need to solve the equation:

23 - (1.5 * n) + (2 * (n / 2)) = 16.5

Let's simplify the equation:

23 - 1.5n + n = 16.5
23 - 0.5n = 16.5
-0.5n = 16.5 - 23
-0.5n = -6.5

Now, let's solve for n by dividing both sides of the equation by -0.5:

n = (-6.5) / (-0.5)
n = 13

Therefore, the tank will contain 16.5 gallons after 13 weeks.

Note: If you prefer to calculate the remaining time in terms of months or years, divide the number of weeks by 4 (for months) or 52 (for years).