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:
- A small tank with 10 gallons can support 12 small fish.
- 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.
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