Skip to content

Instantly share code, notes, and snippets.

@przadka
Created February 1, 2025 16:35
Show Gist options
  • Save przadka/8f021b47eec17ad144a24572d075028b to your computer and use it in GitHub Desktop.
Save przadka/8f021b47eec17ad144a24572d075028b to your computer and use it in GitHub Desktop.
r1-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>
To determine the number of starfish in the aquarium, let's break down the problem step by step.
### Step 1: Define Variables
- Let \( s \) represent the number of starfish.
- Let \( o \) represent the number of octopuses.
### Step 2: Understand the Arm Counts
- Each starfish has **5 arms**.
- Each octopus has **8 arms**.
### Step 3: Set Up the Equation
The total number of arms from all animals is **41**. Therefore:
\[
5s + 8o = 41
\]
### Step 4: Solve for Possible Integer Solutions
We need to find non-negative integers \( s \) and \( o \) that satisfy the equation.
Let's solve for \( s \):
\[
5s = 41 - 8o \\
s = \frac{41 - 8o}{5}
\]
For \( s \) to be an integer, \( 41 - 8o \) must be divisible by **5**.
### Step 5: Find Valid Values of \( o \)
Let's test possible values of \( o \):
1. **If \( o = 2 \):**
\[
s = \frac{41 - 8(2)}{5} = \frac{41 - 16}{5} = \frac{25}{5} = 5
\]
This gives \( s = 5 \), which is a valid integer.
2. **If \( o = 7 \):**
\[
s = \frac{41 - 8(7)}{5} = \frac{41 - 56}{5} = \frac{-15}{5} = -3
\]
Negative number of starfish is not possible.
3. **If \( o = 0 \):**
\[
s = \frac{41 - 8(0)}{5} = \frac{41}{5} = 8.2
\]
Not an integer.
4. **If \( o = 1 \):**
\[
s = \frac{41 - 8(1)}{5} = \frac{33}{5} = 6.6
\]
Not an integer.
5. **If \( o = 3 \):**
\[
s = \frac{41 - 8(3)}{5} = \frac{41 - 24}{5} = \frac{17}{5} = 3.4
\]
Not an integer.
6. **If \( o = 4 \):**
\[
s = \frac{41 - 8(4)}{5} = \frac{41 - 32}{5} = \frac{9}{5} = 1.8
\]
Not an integer.
7. **If \( o = 5 \):**
\[
s = \frac{41 - 8(5)}{5} = \frac{41 - 40}{5} = \frac{1}{5} = 0.2
\]
Not an integer.
8. **If \( o = 6 \):**
\[
s = \frac{41 - 8(6)}{5} = \frac{41 - 48}{5} = \frac{-7}{5} = -1.4
\]
Negative number of starfish is not possible.
### Step 6: Conclusion
The only valid solution is when \( o = 2 \) and \( s = 5 \).
\[
\boxed{5}
\]
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment