let

f = the age of frank

b = the age of his brother

Frank is 4 times as old as his brother:

f = 4b

the difference in their ages is 24 years:

f - b = 24

by solving the system of equations:

f = 4b

f - b = 24

we find:

f = 32 years

b = 8 years

click here to see the step by step solution of the system of equations:

Frank is 32 years old and his brother is 8 years old.