Question

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

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

Set up the proportion: 30/54 = _

Cross Multiply: 30x = _

Solve for x: x = _ feet

Answer 1

To set up the proportion, we need to identify the equivalent parts of the distances. Given the relationship between the distances, the setup should look something like this:

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

Here, 30 feet represents the distance from the whales to the sharks (the first segment) and 54 feet represents the distance from the penguins to the fish tank (the second segment).

To find the distance \(d\) between the penguins and the fish tank, we will cross-multiply:

\[
30 \cdot d = 54 \cdot x
\]

Now we solve for \(x\) (the unknown distance).

1. **Cross Multiply:**
\(30d = 54x\)

2. **Solve for d (the distance between penguins and fish tanks):**
Rearranging the equation for \(d\):
\[
d = \frac{54x}{30}
\]

We can simplify this:
\[
d = \frac{54}{30}x
\]
\[
d = \frac{9}{5}x
\]

Here, if you're tasked with finding just \(x\) and you have a particular value for the proportion that we need to find as \(d\), you should know what \(x\) is first. Usually, \(x\) is a known distance.

Without knowing the actual value of \(x\) in any feet, let's say you find or use a specific value for better context.

If you put your \(x\) value to calculate \(d\) right:
- If we have \(x = 1\):
\[
d = \frac{9}{5}(1) = \frac{9}{5} \text{ feet} = 1.8 \text{ feet}
\]

So if you provide the value of x, you could plug that in to find the exact distance!

However, in the context of your initial structure, you need to provide an additional distance (from the original problem context) for \(x\) to finalize and check the distance value effectively.