This is a classic unit conversion problem that tests your ability to track multiple conversions simultaneously. The key concept here is dimensional analysis—treating units like algebraic variables that cancel out.
Step 1: Identify what we're converting
We start with: 1000p dollars for a square feet
We want: francs per square meter
Step 2: Convert the price from dollars to francs
If 1 dollar = f francs, then:
1000p dollars = 1000pf francs
Step 3: Convert square feet to square meters
This is where most students make mistakes. Since 1 foot ≈ 30 cm = 0.3 meters:
- 1 square foot = (0.3)2 = 0.09 square meters
- Therefore: a square feet = 0.09a square meters
Step 4: Calculate price per square meter
Price per square meter = Total price ÷ Total area
= 1000pf francs ÷ 0.09a square meters
= 1000pf/(0.09a)
= 1000pf/(9a/100)
= 1000pf × (100/9a)
= 100,000pf/9a
≈ 11,000pf/a
Answer: B
Common trap: Students often forget to square the conversion factor when dealing with area. Converting feet to meters requires using (0.3)2, not just 0.3. The answer choices anticipate this—option D (90,000p/fa) is what you'd get if you forgot to square the conversion.
Takeaway: On unit conversion problems with area or volume, always square or cube your linear conversion factors accordingly.