Final answer:
The age of the youngest brother is 26 years old, determined by setting up an equation where the youngest brother's age is x and solving for x considering the relationships and information provided.
Step-by-step explanation:
The question asks us to determine the age of the youngest brother given that the ages of three brothers are consecutive even integers and that three times the age of the youngest exceeds the oldest brother's age by 48 years.
Let's denote the age of the youngest brother as x. Considering the ages are consecutive even integers, the next brother would be x+2 and the oldest x+4. The problem states that 3x exceeds x+4 by 48 years.
Setting up the equation:
3x = (x + 4) + 48
2x = 52
x = 26
Therefore, the age of the youngest brother is 26 years old.