Final answer:
Phil is 32 years old and Stanley is 8 years old. To determine this, we set up equations based on the given age relationship and solved them step by step.
Step-by-step explanation:
Let's denote Stanley's current age as S and Phil's current age as P. According to the problem, Phil is 24 years older than Stanley, which we can represent as P = S + 24. Four years ago, Phil's age was P - 4 and Stanley's was S - 4. According to the second condition, four years ago, Phil was 7 times as old as Stanley, leading to the equation P - 4 = 7(S - 4).
To find their present ages, we'll first use the second equation to express P in terms of S:
- P - 4 = 7S - 28
- P = 7S - 28 + 4
- P = 7S - 24
Next, substitute the expression for P from the first condition into the obtained equation:
- S + 24 = 7S - 24
- 6S = 48
- S = 8
Now that we have Stanley's age, we can find Phil's age:
- P = S + 24
- P = 8 + 24
- P = 32
Therefore, Phil is 32 years old and Stanley is 8 years old, which corresponds to option (b).