Rosamaria is setting up a 20 gallon saltwater fish tank that needs to have a salt content of 35%. If Rosamaria has water that has 2.5% salt and water that has 3.7% salt, how many gallons of the water with 3.7% salt content should Rosamaria use?

Let's denote the volume of the 2.5% salt water by \( x \) gallons and the volume of the 3.7% salt water by \( y \) gallons.

We need to set up the following equations based on the given conditions:

1. The total volume of the tank is 20 gallons:
   \[
   x + y = 20
   \]

2. The total amount of salt in the tank must be 35% of 20 gallons, which is \( 0.35 \times 20 \) gallons of salt:
   \[
   0.025x + 0.037y = 0.35 \times 20
   \]

First, calculate the total amount of salt needed:
\[
0.35 \times 20 = 7 \text{ gallons of salt}
\]

Now, we have the system of equations:
\[
x + y = 20
\]
\[
0.025x + 0.037y = 7
\]

Solve the first equation for \( x \):
\[
x = 20 - y
\]

Substitute this into the second equation:
\[
0.025(20 - y) + 0.037y = 7
\]

Distribute and combine like terms:
\[
0.025 \times 20 - 0.025y + 0.037y = 7
\]
\[
0.5 - 0.025y + 0.037y = 7
\]
\[
0.012y + 0.5 = 7
\]

Subtract 0.5 from both sides:
\[
0.012y = 6.5
\]

Solve for \( y \):
\[
y = \frac{6.5}{0.012}
\]
\[
y = 541.67 \text{ gallons}
\]

This result suggests that using these specific salt concentrations, it is impossible to achieve the desired 35% salt content in a 20-gallon tank. It indicates that there's a need to either use different concentrations of salt water or the question needs rechecking for possible inaccuracies.

Would you like further details on this solution or need help with another aspect of the problem?

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**Here are 8 related questions to expand your knowledge:**

1. How do you determine the salt content required for different sizes of saltwater tanks?
2. What are the implications of having too high or too low salt content in a fish tank?
3. Can you use a different combination of salt percentages to achieve a 35% salt solution?
4. How do you mix solutions of different concentrations to achieve a desired concentration?
5. What are some methods to adjust the salt content in an existing fish tank?
6. How do different types of salt affect the salinity of water?
7. What is the importance of maintaining correct salt levels in a saltwater aquarium?
8. How do environmental factors influence the salt content in a fish tank?

**Tip:** Always double-check your equations and units when solving mixture problems to ensure accuracy.

Learn how to calculate the amount of water with 3.7% salt needed to achieve a 35% salt content in a 20-gallon saltwater fish tank. This problem involves linear equations and percentage calculations. Suitable for advanced high school students.

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