One unit of a peso in a Latin American country was defined as equivalent to 12 grains of "fine" (pure) gold, while one unit of its neighboring countries’ currency, a dollar, was defined as equivalent to 18 grains of "fine" (pure) gold. Using the gold par value concept (with 480 grains in an ounce), the exchange rate for converting the peso to the dollar is单项选择题
A
1 peso = 1.5 dollars.
B
1 peso = 1 dollar.
C
1.5 pesos = 1 dollar.
D
3 pesos = 2 dollars.
E
2 pesos = 1 dollar.

Question

One unit of a peso in a Latin American country was defined as equivalent to 12 grains of "fine" (pure) gold, while one unit of its neighboring countries’ currency, a dollar, was defined as equivalent to 18 grains of "fine" (pure) gold. Using the gold par value concept (with 480 grains in an ounce), the exchange rate for converting the peso to the dollar is单项选择题

A

1 peso = 1.5 dollars.

B

1 peso = 1 dollar.

C

1.5 pesos = 1 dollar.

D

3 pesos = 2 dollars.

E

2 pesos = 1 dollar.

BlackTom AI · Accepted Answer

One peso contains 12 grains of pure gold and one dollar contains 18 grains, so the exchange rate is determined by the ratio of gold content.

Compute values in grains and ounces (intermediate step using 480 grains/ounce to show cancellation):
- Peso gold per unit = 12 grains = 12/480 = 0.025 ounce of fine gold.
- Dollar gold per unit = 18 grains = 18/480 = 0.0375 ounce of fine gold.
Exchange rate (peso → dollar) = (peso gold) / (dollar gold) = 12 / 18.

Step-by-step arithmetic:
1. 12 / 18 = 2 / 3, so 1 peso = 2/3 dollar (≈ $0.6667).
2. Invert to express dollars in pesos: 1 dollar = 18 / 12 = 3 / 2 = 1.5 pesos.
3. Multiply both sides by 2 to get whole numbers: 2 dollars = 3 pesos, which is the same as 3 pesos = 2 dollars.

Why the correct answer is correct:
- The gold-par exchange rate is proportional to gold content. Because a dollar contains 1.5 times as much gold as a peso (18 ÷ 12 = 1.5), one dollar must be worth 1.5 pesos, equivalently 3 pesos equal 2 dollars. This matches the provided correct choice.

Why the other answer choices are incorrect:
- "1 peso = 1.5 dollars." This would imply a peso contains more gold than a dollar; it contradicts 12 < 18 grains, so false.
- "1 peso = 1 dollar." Implies equal gold content; false.
- "1.5 pesos = 1 dollar." This statement is numerically equivalent to the correct answer (1.5 pesos = 1 dollar ⇔ 3 pesos = 2 dollars). It is therefore correct in value but not the phrasing chosen as the official answer.
- "2 pesos = 1 dollar." Implies 1 peso = $0.50, which is incorrect.