Final answer:
The question involves setting up and solving equations to find the current age of Darlene and her brother. Darlene is 10 years old currently, and her brother is 40 years old. In five years, his age will be three times hers.
Step-by-step explanation:
Darlene's brother is now 4 times as old as she is, and in 5 years, his age will be thrice hers. Let d represent Darlene's age now. To solve this problem, we set up two equations based on the information given. First, we express Darlene's brother's age in terms of Darlene's age:
Brother's age = 4d
In five years, Darlene will be d + 5 years old, and her brother will be 4d + 5 years old. According to the second part of the problem:
4d + 5 = 3(d + 5)
To solve for d, we expand and simplify the equation:
4d + 5 = 3d + 15
4d - 3d = 15 - 5
d = 10
So, Darlene is currently 10 years old, and her brother is 40 years old. In five years, she will be 15, and he will be 45, which is indeed three times her age at that time.