Question

Phil is 24 years older than Stanley. Four years ago, he was 7 times as old as Stanley was then. Find their present ages.

a) Phil is 28 years old and Stanley is 4 years old.
b) Phil is 32 years old and Stanley is 8 years old.
c) Phil is 36 years old and Stanley is 12 years old.
d) Phil is 40 years old and Stanley is 16 years old.

Answer 1

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).