A U.S. dollar equals 0.716 European euros, and a Japanese yen equals 0.00776 European euros. How many U.Sgt dollars equal a Japanese yen?

Options

A. 0.0056
B. 0.011
C. 94.2
D. 179.98

Explanation

To find out how many U.S. dollars equal a Japanese yen, we can follow these steps:

### Step 1: Understand the given exchange rates
We know:
- 1 U.S. dollar (USD) = 0.716 European euros (EUR)
- 1 Japanese yen (JPY) = 0.00776 European euros (EUR)

### Step 2: Find the value of 1 Euro in terms of U.S. dollars
To find how many U.S. dollars equal 1 Euro, we can take the reciprocal of the first exchange rate:
\[ 1 \text{ Euro} = \frac{1}{0.716} \text{ USD} \]
Calculating this gives:
\[ 1 \text{ Euro} \approx 1.40 \text{ USD} \]

### Step 3: Find the value of 1 Euro in terms of Japanese yen
Similarly, to find how many Japanese yen equal 1 Euro, we take the reciprocal of the second exchange rate:
\[ 1 \text{ Euro} = \frac{1}{0.00776} \text{ JPY} \]
Calculating this gives:
\[ 1 \text{ Euro} \approx 128.87 \text{ JPY} \]

### Step 4: Set the two expressions for 1 Euro equal to each other
Since both expressions represent the same value (1 Euro), we can set them equal:
\[ 1.40 \text{ USD} = 128.87 \text{ JPY} \]

### Step 5: Find the value of 1 Japanese yen in terms of U.S. dollars
To find how many U.S. dollars equal 1 Japanese yen, we can rearrange the equation:
\[ 1 \text{ JPY} = \frac{1.40 \text{ USD}}{128.87} \]
Calculating this gives:
\[ 1 \text{ JPY} \approx 0.01087 \text{ USD} \]

### Final Answer
Thus, approximately:
\[ 1 \text{ Japanese yen} \approx 0.01087 \text{ U.S. dollars} \]