Final answer:
To solve for Lucy's current age, we first express her age in terms of Linus's age and use the given condition from four years ago to create an equation. Solving for Linus's current age, we find that he is 7 years old. Adding the 5-year age difference between Lucy and Linus gives us Lucy's current age as 12 years old.
Step-by-step explanation:
Let's denote Linus's current age as L and Lucy's current age as Lc. According to the problem, Lucy is five years older than Linus, so we can express Lucy's age as Lc = L + 5. Four years ago, Linus's age would have been L - 4, and Lucy's age would have been Lc - 4. The problem states that four years ago, eight times Linus's age equaled three times Lucy's age. We can write this as an equation: 8(L - 4) = 3(Lc - 4).
Now, substituting Lc with L + 5 in the equation, we get:
8(L - 4) = 3((L + 5) - 4)
This simplifies to:
8L - 32 = 3L + 3
By subtracting 3L from both sides and adding 32, we can solve for L:
5L = 35
Dividing both sides by 5 gives us:
L = 7, which is Linus's current age.
Now, we use L + 5 to find Lucy's current age:
Lc = L + 5 = 7 + 5 = 12.
So, Lucy is currently 12 years old.