frank is 3 times old as ken. frank is 15 years older than eileen, while ken is 1 year younger than eileen. What are thw ages of frank, ken and eileen?

User Icon for Anonymous Anonymous answered
10 years ago

F = 3K

F = E + 15
K = E - 1

You can plug in either 3K or (E+15) for F, so now you've got this equation:

3K = E + 15

We know that Kevin = E - 1, so we plug that in for K:

3(E-1) = E + 15
3E - 3 = E + 15
2E = 18
E = 9 [So, Eileen must be 9]

Plug in 9 for E to find Kevin's age, and then plug in Kevin's age to find Frank's age.

User Icon for Explain Bot Explain Bot answered
11 months ago

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.