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Created February 1, 2025 16:12
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o3-mini-aquarium
<USER>
### 2. Aquarium
In the aquarium, there are octopuses with eight arms and starfish with five arms.
**How many starfish are there in the aquarium if the total number of arms of all the animals living in it is 41?**
<ASSISTANT>
Let \( x \) be the number of octopuses and \( y \) be the number of starfish. Each octopus has 8 arms and each starfish has 5 arms, so the total number of arms is given by:
\[
8x + 5y = 41
\]
We need to find nonnegative integers \( x \) and \( y \) that satisfy this equation.
### Step 1: Solve for \( y \)
We can start by testing small values of \( x \):
1. **For \( x = 0 \):**
\[
8(0) + 5y = 41 \implies 5y = 41 \implies y = \frac{41}{5} = 8.2 \quad \text{(not an integer)}
\]
2. **For \( x = 1 \):**
\[
8(1) + 5y = 41 \implies 8 + 5y = 41 \implies 5y = 33 \implies y = \frac{33}{5} = 6.6 \quad \text{(not an integer)}
\]
3. **For \( x = 2 \):**
\[
8(2) + 5y = 41 \implies 16 + 5y = 41 \implies 5y = 25 \implies y = 5
\]
Here, \( y = 5 \) is an integer.
### Step 2: Verify the Solution
With \( x = 2 \) and \( y = 5 \):
\[
8(2) + 5(5) = 16 + 25 = 41
\]
The equation holds true.
### Conclusion
The number of starfish in the aquarium is:
\[
\boxed{5}
\]
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