The Balanced Aquarium

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Ms. Johnson’s class is learning about equilibrium using a small aquarium. The aquarium has:

10 small fish that eat algae
Algae that grows constantly

Every day:

Each fish eats 2 units of algae
The algae grows by 25 units

Ms. Johnson explains that for the aquarium to be in equilibrium, the amount of algae eaten should equal the amount of algae that grows each day.

Questions:

How many units of algae do all the fish eat in one day?
Is the aquarium in equilibrium? Why or why not?
If the aquarium is not in equilibrium, how many fish would be needed to make it balanced?
If we kept 10 fish, how much should the algae grow each day to reach equilibrium?
Why do you think it’s important for an aquarium to be in equilibrium?

Solution

1. Algae eaten by all fish in one day:
10 fish × 2 units of algae = 20 units of algae

2. The aquarium is not in equilibrium because:
Algae eaten (20 units) ≠ Algae growth (25 units)
The algae is growing faster than it’s being eaten.

3. Fish needed for equilibrium:
We need the fish to eat 25 units of algae.
25 units ÷ 2 units per fish = 12.5 fish
Since we can’t have half a fish, we round up to 13 fish for slightly more algae consumption.

4. Algae growth for equilibrium with 10 fish:
10 fish × 2 units of algae = 20 units
The algae should grow by 20 units each day for equilibrium.

5. Importance of equilibrium in an aquarium:

Keeps the water clean and healthy for the fish
Prevents too much algae from growing and taking over
Ensures the fish have enough food to eat
Maintains a stable environment for all living things in the aquarium
Reduces the need for human intervention to clean or adjust the aquarium