Final answer:
Maggie's brother is 14 years younger than four times her age. The sum of their ages is 61. Maggie is 15 years old.
Step-by-step explanation:
Let's represent Maggie's age as x. According to the given information, her brother's age is 4x - 14.
The sum of their ages is 61, so we can write the equation: x + (4x - 14) = 61.
Simplifying the equation, we have 5x - 14 = 61.
Adding 14 to both sides gives us 5x = 75.
Dividing both sides by 5, we find that x = 15.
Therefore, Maggie is 15 years old. Option D is the correct answer.