https://file.aiquickdraw.com/mathbot/file/17255516327654rwd9f6r.jpg

Let's analyze the problem described in the image:

- The total number of fish in the aquarium is **364**.
- The number of angelfish is **1/2** of the number of guppies.
- The ratio of the number of angelfish to the number of guppies is **3:4**.

### Part (a)
We are asked to find the ratio of the number of angelfish to the number of goldfish.

Let's define:
- **A** as the number of angelfish.
- **G** as the number of guppies.
- **O** as the number of goldfish.

### Step 1: Establish relationships
From the information given:
1. **A = (1/2) G** (half the number of guppies).
2. The ratio of angelfish to guppies is given as 3:4. Hence, we can say that:
   \[
   \frac{A}{G} = \frac{3}{4}
   \]

3. The total number of fish is:
   \[
   A + G + O = 364
   \]
   
### Step 2: Solve the system of equations
Now, I'll solve these relationships step by step.

Let me calculate the next steps.It seems there was a complication with solving the system of equations directly. I'll revisit the steps to ensure everything is set up correctly.

### Clarification of the situation:
We are provided:
1. The ratio of angelfish to guppies is **3:4**, so:
   \[
   \frac{A}{G} = \frac{3}{4}, \quad \text{or} \quad A = \frac{3}{4}G
   \]
   
2. The total number of fish is **364**, so the equation becomes:
   \[
   A + G + O = 364
   \]

From the ratio, we also know:
\[
A = \frac{3}{4}G
\]

Let me substitute this into the total number of fish equation and solve.The solution shows that the number of angelfish (\(A\)) and guppies (\(G\)) depend on the number of goldfish (\(O\)).

We have:
- \( A = 104 - 0.286 \times O \)
- \( G = 208 - 0.571 \times O \)

To fully determine the values, we need to know the exact number of goldfish. Could you clarify if any additional details about the number of goldfish were given?

Let me know if you want further clarifications, and here are 5 questions to extend this problem:

1. What would happen if the total number of fish changed but the ratios remained the same?
2. Can we derive a different equation if we assume the number of goldfish is half of another fish type?
3. How do the relationships between the different fish types affect the total count?
4. Can you explain how ratios impact real-world population problems like this one?
5. What if there were another fish species added to the equation?

**Tip:** When solving multiple equations, simplifying one in terms of another can make it easier to substitute and reduce complexity.

There are a total of 364 fish in an aquarium. Half of the number of angelfish is 3/5 times the number of guppies. The ratio of the number of goldfish to the number of angelfish is 3:4. How many more angelfish than goldfish are there in the aquarium?

Learn how to solve a mathematical problem involving fish populations in an aquarium. The problem covers concepts of ratio and proportion, algebra, and linear equations. Students will explore relationships between different types of fish, such as guppies, angelfish, and goldfish. Suitable for Grades 7-9.

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