Final answer:
By setting up equations based on the relationships between the ages of Felix, Jake, and Tom, and solving for their ages, we find that Felix is 24, Jake is 19, and Tom is 94, making option A the correct answer.
Step-by-step explanation:
The problem given is an algebraic age problem that can be solved by setting up equations based on the information provided. We are told that Tom has two grandsons, Felix and Jake. Jake is 5 years older than half of Felix’s age, and Tom is 4 times Jake's age. The sum of all their ages is 137. To solve for their ages, let's denote Felix's age as F, Jake's age as J, and Tom's age as T. Jake is 5 years older than half of Felix’s age: J = (1/2)F + 5, Tom is 4 times Jake’s age: T = 4J, The sum of all their ages is 137: F + J + T = 137. Now we can substitute J and T into the third equation using the first two equations: F + ((1/2)F + 5) + 4((1/2)F + 5) = 137. Therefore, the correct answer is A) Felix: 24, Jake: 19, Tom: 94.