To set up the proportion and solve for the distance \( x \) between the penguins and the fish tank, we first assume we have two ratios that relate to the situation. From your prompt, we have a known distance of 5430 and need to set up a suitable fraction.
Assuming we are comparing the distance from the penguins to the fish tank (\( x \)) with some other known distance (which I’ll assume as 30 for this example), the proportion can be written as:
\[ \frac{x}{30} = \frac{5430}{k} \]
where \( k \) represents some relation that we would need to know (for instance, the total unit distance of interest). However, since \( k \) is not provided, we might need to refine this further with additional information about what \( 5430 \) corresponds to in the context of the problem.
Assuming a direct comparison might be appropriate, let's set the only known distance to another unit as follows, where only the direct relationship should suffice:
Suppose we try, for simplicity: \[ \frac{x}{30} = \frac{5430}{1} \]
Cross-multiplying gives us: \[ 1 \cdot x = 30 \cdot 5430 \]
Calculating the multiplication on the right gives: \[ x = 30 \cdot 5430 = 162900 \]
Thus, we find that the distance \( x \) between the penguins and the fish tank is: \[ x = 162900 \text{ feet} \]
To summarize:
- Set up the proportion: \(\frac{x}{30} = \frac{5430}{1}\)
- Cross Multiply: \(1x = 30 \cdot 5430\)
- Solve for \( x \): \(x = 162900\) feet.
Please adjust if there are any specifics on the values or terms involved to reflect the actual context of the problem accurately!