Let A be Amy's present age, P be Phil's present age.

Then the first equation is

A = P - 24.       (1)     ("Amy was born when Phil was 24 years old.")

When Amy will be 3 times as old as she is today ?  -  In 2A years.

At that time ("in 2A years") Phil's age will be (P + 2A).

Hence, the second equation is

3(3A) = P + 2A.    (2)     ("When Amy is 3 times as old as she is today, Phil will be 3 times as old as Amy.")

From (2), 7A = P.

Now substitute this expression P = 7A into (1). You will get

A = 7A - 24  --->  24 = 6A  --->  A =   = 4.

Answer.  Ami's current age is 4 years. Phil's present age is P =A + 24 = 4 + 24 = 28 years.

Let Phil’s age be P, and Amy’s, A

Then A = P – 24



When Amy is 3 times her current age, she will be her current age, plus 2 times her current age, or P – 24 + 2A =====> P – 24 + 2(P – 24), or P – 24 + (2P – 48)

Therefore, Amy will be 3(P – 24), or 3P – 72, in (2P – 48) years

Also, in (2P – 48) years, Phil will be P + 2P – 48, or (3P – 48) years-old



We then get: 3P – 48 = 3(3P – 72)

3P – 48 = 9P – 216

3P – 9P = - 216 + 48

– 6P = - 168

P, or Phil is:  

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