To solve this problem, we can use a system of equations. Let's assign variables to each person's age:
Let's say Frank's age is F, Ken's age is K, and Eileen's age is E.
From the problem statement, we have the following information:
1. Frank is 3 times as old as Ken: F = 3K.
2. Frank is 15 years older than Eileen: F = E + 15.
3. Ken is 1 year younger than Eileen: K = E - 1.
Now we can solve this system of equations to find the ages of Frank, Ken, and Eileen.
First, let's rewrite equation 1 and equation 2 in terms of K and E:
1. F = 3K becomes F - 3K = 0.
2. F = E + 15 remains the same.
Now, substitute equation 2 into equation 1 to eliminate F:
(E + 15) - 3K = 0.
E + 15 - 3K = 0.
E - 3K = -15.
Substitute the value of E - 1 for K into this equation:
E - 3(E - 1) = -15.
E - 3E + 3 = -15.
-2E = -18.
E = 9.
Now that we have Eileen's age (E = 9), substitute this value back into equation 3 to find Ken's age:
K = E - 1.
K = 9 - 1.
K = 8.
Finally, substitute E = 9 and K = 8 into equation 2 to find Frank's age:
F = E + 15.
F = 9 + 15.
F = 24.
Therefore, Frank is 24 years old, Ken is 8 years old, and Eileen is 9 years old.