A certain municipality recently changed the fines levied for being caught exceeding the posted speed limit. The fine is €10...

Phase 1: Owning the Dataset

Visualization

Let's create a number line to visualize the speed limit and fines:

Speed (kph):  0 -------- 130 ---|--- 140 --- 150 --->
                   Speed Limit   |   +10     +20
                                 |
Fine (Euro):           Euro0          Euro0   Euro100    Euro200

Key Information

• Speed limit: 130 kph
• Fine structure: Euro10 for every 1 kph over the limit
• We need to find a speed > 130 kph and its corresponding fine

Phase 2: Understanding the Question

We need to select TWO values that work together:

1. A speed (in kph) that exceeds 130 kph
2. The total fine (in euros) for that speed

Fine Formula

For any speed exceeding 130 kph:

Total Fine = \(\mathrm{Euro10 \times (Speed - 130)}\)

Available Choices

5, 50, 100, 130, 140, 150

Phase 3: Finding the Answer

Step 1: Identify Valid Speeds

From our choices, which speeds exceed 130 kph?

• 5 kph: No (< 130)
• 50 kph: No (< 130)
• 100 kph: No (< 130)
• 130 kph: No (equals limit, not exceeding)
• 140 kph: Yes (exceeds by 10 kph)
• 150 kph: Yes (exceeds by 20 kph)

Step 2: Calculate Fines for Valid Speeds

For 140 kph:

• Exceeds limit by: \(\mathrm{140 - 130 = 10}\) kph
• Fine = \(\mathrm{Euro10 \times 10 = Euro100}\)
• Is Euro100 in our choices? Yes! ✓

Stop here - we found our answer.

(For completeness: 150 kph would result in Euro200, which isn't available)

Phase 4: Solution

Final Answer

• Speed in kph: 140
• Total fine in euros: 100

The automobile was traveling at 140 kph (10 kph over the limit), resulting in a fine of Euro100.