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To solve this problem, we can break it down step by step:

### 1. Ratio of Sharks to Dolphins
The ratio of sharks to dolphins is given as **3:5**. We also know that there are **6 sharks** in the aquarium. Using this ratio, we can find the number of dolphins.

Let the number of dolphins be \( x \).
\[
\frac{3}{5} = \frac{6}{x}
\]
By cross-multiplying, we get:
\[
3x = 30
\]
Solving for \( x \):
\[
x = 10
\]
Thus, there are **10 dolphins** in the aquarium.

### 2. Ratio of Dolphins to Starfish
The ratio of dolphins to starfish is given as **2:7**. We now know there are **10 dolphins**. Using this ratio, we can find the number of starfish.

Let the number of starfish be \( y \).
\[
\frac{2}{7} = \frac{10}{y}
\]
Cross-multiplying:
\[
2y = 70
\]
Solving for \( y \):
\[
y = 35
\]
Thus, there are **35 starfish** in the aquarium.

### Final Answer:
There are **35 starfish** in the aquarium.

Do you have any questions or need further details? Here are some related questions for further exploration:

1. What if there were 9 sharks? How many starfish would be in the aquarium then?
2. If the ratio of sharks to dolphins changed to 4:5, how would the number of starfish be affected?
3. Can you derive a direct ratio between sharks and starfish based on the two given ratios?
4. How many animals (sharks, dolphins, and starfish) are there in total in the aquarium?
5. If 5 starfish were removed from the aquarium, what would the new ratio of dolphins to starfish be?

**Tip:** When solving ratio problems, always set up proportions based on the given ratios and known quantities, then solve for the unknowns using cross-multiplication.

In an aquarium, the ratio of sharks to dolphins is 3:5 and the ratio of dolphins to starfish is 2:7. There are 6 sharks in the aquarium. How many starfish are there?

In this problem, you will learn how to solve a ratio problem involving sharks, dolphins, and starfish in an aquarium. We start with the ratios 3:5 for sharks to dolphins and 2:7 for dolphins to starfish, with 6 sharks given. Follow a detailed step-by-step solution to find out how many starfish there are.

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