Final answer:
The value of the yen in euros is calculated using the given exchange rates, resulting in 0.0087 euros per yen, which corresponds to option 4.
Step-by-step explanation:
To determine the value of the yen in euros, we use the given exchange rates of $1 = 0.85 euros and $1 = 98 yen. We need to find out how much 1 yen is worth in euros. The first step is to calculate the value of 1 yen in dollars, which is $1 / 98 yen. Then, we convert the dollar to euros using the given rate of $1 = 0.85 euros. Hence, the value of 1 yen in euros is ($1 / 98) * 0.85 euros. A calculation provides the answer:
((1 / 98) * 0.85 euros) = 0.008673469 euros per yen,
which can be rounded to 0.0087 euros per yen. Therefore, the correct answer is option 4.