We are given that 2.5 centimeters on the map represents 15 kilometers in real life. We need to find how many kilometers are represented by 17.5 centimeters.

This is a proportion problem. Let's set up the proportion:

$\frac{2.5 \, \text{cm}}{15 \, \text{km}} = \frac{17.5 \, \text{cm}}{x \, \text{km}}$

To solve for $x$, we can cross-multiply:

$2.5x = 17.5 \times 15$

Now, let's calculate this:

$x = \frac{17.5 \times 15}{2.5}$

Let's compute the value of $x$.The number of actual kilometers represented by 17.5 centimeters on the map is 105 kilometers.

Would you like further details or have any additional questions?

Here are five related questions:

1. How would the scale change if 5 centimeters represented 30 kilometers?
2. What would the map scale be if 10 centimeters represented 100 kilometers?
3. How can you convert centimeters to kilometers if given a different scale ratio?
4. How does changing the scale affect the accuracy of real-world distance estimations on maps?
5. What are some real-life applications of map scaling?

Tip: When solving proportion problems, always set up the ratio carefully and ensure units are consistent before solving.