Question

The local pet store advises that the number of small fish in a tank should be proportional to the gallons of water in the tank. A small tank with 10 gallons of water can support 12 small fish. A medium tank with 20 gallons of water can support 24 small fish.
How many small fish should be in a large tank with 50 gallons of water? Show all your work.

Answer 1

To find out how many small fish can be supported in a large tank with 50 gallons of water, we can first establish the relationship between the gallons of water and the number of small fish.

From the information given:

1. A small tank with 10 gallons can support 12 small fish.
2. A medium tank with 20 gallons can support 24 small fish.

Let's first determine the rate of fish per gallon of water based on the information provided.

**Finding the rate of fish per gallon:**

For the small tank:
- 10 gallons → 12 fish.
- The fish per gallon = \( \frac{12 \text{ fish}}{10 \text{ gallons}} = 1.2 \text{ fish/gallon} \).

For the medium tank:
- 20 gallons → 24 fish.
- The fish per gallon = \( \frac{24 \text{ fish}}{20 \text{ gallons}} = 1.2 \text{ fish/gallon} \).

Thus, the rate of 1.2 fish per gallon is consistent across both tanks.

**Finding the number of fish in a large tank with 50 gallons:**

We will use the rate of 1.2 fish per gallon to determine how many fish can be supported in the large tank:

\[
\text{Number of fish} = \text{gallons of water} \times \text{fish per gallon}
\]
\[
\text{Number of fish} = 50 \text{ gallons} \times 1.2 \text{ fish/gallon}
\]
\[
\text{Number of fish} = 60 \text{ fish}
\]

Therefore, a large tank with 50 gallons of water should ideally support **60 small fish**.