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In the map below, the path from the whales to the sharks is parallel to the path from the penguins to the fish tanks.

Whales, 54 feet, Sharks, Dolphins, Penguins, x feet, and Fish Tanks



Set up and solve the proportion to find the distance between the penguins and the fish tank.

(3 points)
Set up the proportion: 3054=



NOTE: Type the correct fraction into the box to receive credit.

Cross Multiply: 30x=



NOTE: Type the correct numerical answer into the box to receive credit.

Solve for x: x=

feet

NOTE: Type the correct numerical answer into the box to receive credit.

3 answers

To solve this problem, we need to set up a proportion based on the information provided. The path from the whales to the sharks (54 feet) is parallel to the path from the penguins to the fish tanks (x feet).

Since the paths are parallel, we can set up the proportion as follows:

\[ \frac{54}{x} = \frac{30}{54} \]

This means that the length from the whales to the sharks (54 feet) is to the distance from the penguins to the fish tanks (x feet) as the length of the segment from another reference point (here, 30 feet, presumably corresponding to another identified distance).

Now we can cross multiply to solve for x:

Cross Multiply: \[ 54 \cdot 30 = 54 \cdot x \]

Calculating the left side: \[ 1620 = 54x \]

Now, to solve for x, we divide both sides by 54:

\[ x = \frac{1620}{54} \]

Calculating this gives:

\[ x = 30 \]

Thus, the distance between the penguins and the fish tanks is:

\[ \boxed{30} \text{ feet} \]

Summary of answers:

  • Set up the proportion: \(\frac{54}{x} = \frac{30}{54}\)
  • Cross Multiply: \(30x = 1620\)
  • Solve for \(x\): \(x = 30\) feet
wrong

I apologize for the confusion in interpreting the problem. Let’s set up and solve the proportion step by step again.

You mentioned that the path from the whales to the sharks is 54 feet and that there is a parallel path from the penguins to the fish tanks, whose distance we are trying to find, represented by \(x\) feet.

The corresponding segments create the following relationship:

\[ \frac{54 \text{ feet (Whales to Sharks)}}{x \text{ feet (Penguins to Fish Tanks)}} = \frac{30 \text{ feet (reference)}}{(another reference segment)} \]

It looks like the length of the reference segment wasn't given other than 30. To proceed, I'm assuming that 30 was supposed to be paired with something consistent to help establish the proportion. Since we don't have exact information, let me provide a general outline again.

If we had this scenario:

Assuming we have a height comparison, similar to a triangle but with unknown base or height {(just providing variables, not actual numbers}.

  1. Set up the proportion:

If we have: \[ \frac{54}{x} = \frac{30}{some_length} \]

You need to substitute the actual numbers if there’s a specific length for the reference.

  1. Cross-Multiply: \[ 54 \cdot some_length = 30 \cdot x \]

  2. Solve for \(x\): \[ x = \frac{54 \cdot some_length}{30} \]

  3. If possible, replace \( some_length\) with an actual number obtainable in your geometry layout.

Please verify the proportion setup and confirm the side lengths with specific numbers needed. If you provide additional context or elements, we can pinpoint the corrections more precisely!