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?

Question

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?

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2 answers
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Answer 1

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.

Answer 2

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.