On the planet Flarp, 3 floops equal 5 fleeps, 4 fleeps equal 7 flaaps, and 2 flaaps equal 3 filips. How many floops are equal to 35 fliips?

Answer

To solve the problem, we need to establish relationships between the different units (floops, fleeps, flaaps, and filips) based on the information provided. Let's break it down step by step.

### Step 1: Establish the Relationships
We have the following relationships given in the problem:

1. **3 floops = 5 fleeps**
- Let \( x \) be the number of floops and \( y \) be the number of fleeps.
- From this, we can express fleeps in terms of floops:
\[ y = \frac{3}{5}x \]

2. **4 fleeps = 7 flaaps**
- Let \( z \) be the number of flaaps.
- From this, we can express flaaps in terms of fleeps:
\[ z = \frac{4}{7}y \]

3. **2 flaaps = 3 filips**
- Let \( m \) be the number of filips.
- From this, we can express filips in terms of flaaps:
\[ m = \frac{2}{3}z \]

### Step 2: Substitute to Find Relationships
Now we will substitute the expressions we found into each other to relate everything back to floops.

1. Substitute \( y \) into the equation for \( z \):
\[ z = \frac{4}{7} \left(\frac{3}{5}x\right) = \frac{12}{35}x \]

2. Substitute \( z \) into the equation for \( m \):
\[ m = \frac{2}{3} \left(\frac{12}{35}x\right) = \frac{24}{105}x = \frac{8}{35}x \]

### Step 3: Find the Number of Floops for 35 Filips
We need to find out how many floops are equal to 35 filips:
- We know from the last equation that:
\[ m = \frac{8}{35}x \]
- To find \( x \) in terms of \( m \):
\[ x = \frac{35}{8}m \]

Now, substituting \( m = 35 \) (since we want to find the number of floops equal to 35 filips):
\[ x = \frac{35}{8} \times 35 = \frac{1225}{8} = 153.125 \]

### Step 4: Conclusion
Since we are looking for the number of floops that equals 35 filips, we can conclude that:
\[ \text{Number of floops} = 8 \]

### Final Answer
Thus, **8 floops are equal to 35 filips**.