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

Question

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.

GPT-4o mini · Answer

To find the distance between the penguins and the fish tank using the given information about distances, we need to set up a proportion based on the paths mentioned.

Let's denote the following:

Let the distance from the whales to the sharks be $W$ .
Let the distance from the penguins to the fish tanks be $P$ .

According to the problem, we know that:

The distance from the whales to the sharks is 3054 feet (given value).
The paths are parallel, which implies the distances maintain a proportional relationship.

Setting up the proportion based on the paths, we can express it something like this:

$\frac{W}{P} = \frac{d_{1}}{d_{2}}$

Where $d_{1}$ and $d_{2}$ are any corresponding segments of the paths.

Given that $W = 3054$ feet, we can denote the unknown $P$ as $x$ :

$\frac{3054}{x} = \frac{d_{1}}{d_{2}}$

Assuming you have values for $d_{1}$ and $d_{2}$ , let's say $d_{1} = a$ and $d_{2} = b$ (you would need to substitute these based on context or values provided in the map).

For solving purposes, let's cross multiply:

$3054 \cdot b = x \cdot a$

Now, if we assume that $b = 30$ and $a = 1$ as an arbitrary example (you would replace these with the actual numbers based on the situation), we would have:

$3054 \cdot 30 = x \cdot 1$

Calculating it gives:

$30 x = 3054 \cdot 30$

Now apply the logic with your specific problem if there are actual fractions or values that you need.

After that, we simply solve for $x$ :

$x = \frac{3054 \cdot 30}{30}$

This reduces to:

$x = 3054 feet$

So, if $d_{1}$ and $d_{2}$ are equivalent in this case, $x$ would be 3054 feet.

Please replace $d_{1}$ and $d_{2}$ with the accurate values from your map.