If the exchange rate is 80 yen per dollar, then a hotel room in Tokyo that costs 25,000 yen costs $200.

Question

BlackTom AI · Accepted Answer

At an exchange rate of 80 yen per dollar, 25,000 yen converted to dollars is 25,000 ÷ 80 = 312.50, so the statement is false.

1. Relevant knowledge points and concepts
- Exchange rate expressed as "80 yen per dollar" means 1 dollar = 80 yen.
- To convert an amount in yen to dollars, divide the yen amount by the number of yen per dollar (i.e., multiply by the reciprocal: dollars = yen × (1 dollar / 80 yen)).

2. Complete reasoning process step by step
- Start with the hotel price in yen: 25,000 yen.
- Use the exchange rate: 80 yen = 1 dollar.
- Convert by dividing the yen amount by 80 to get dollars.

3. Calculations with intermediate steps
- dollars = 25,000 yen ÷ (80 yen/dollar)
- Compute: 25,000 ÷ 80
- Simplify: 25,000 ÷ 80 = (25,000 ÷ 10) ÷ (80 ÷ 10) = 2,500 ÷ 8
- 2,500 ÷ 8 = 312.5
- Therefore, 25,000 yen = $312.50

4. Why the correct answer is correct
- The statement claimed the 25,000-yen room costs $200 at 80 yen/dollar. Given the correct conversion yields $312.50, the claimed $200 is incorrect. The arithmetic conversion directly demonstrates the mismatch.

5. Why the other option is incorrect
- The "True" option would assert 25,000 yen equals $200. To check: $200 × 80 yen/dollar = 16,000 yen, not 25,000 yen. Thus $200 corresponds to 16,000 yen, so "True" is incorrect.

6. Conclusion confirming the final answer
- The correct response is False, matching the provided answer: the room costs $312.50, not $200.

If the exchange rate is 80 yen per dollar, then a hotel room in Tokyo that costs 25,000 yen costs $200.Single choice

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