Date: Mon, 31 May 1999 19:17:39 -0600 (CST)
Level: Middle

Question:
I have three cousins on my dad's side. The product of their ages is 84. Next year the youngest will be 1/4 the age of the middle cousin. In 2 years from now, the oldest will be twice the current age of the middle. What is the age of my oldest cousin?
I figured out the answer to this by trial and error and i know the oldest has to be 12, middle 7, and youngest 1, because it works out. BUT how do i get to those numbers??? I made up a chart like this:

 now next year 2 years from now youngest x/4 -1 x/4 x/4 +1 middle x-1 x x+1 oldest 2(x-1)-2 2(x-1)-1 2(x-1)

Let x be the age of the middle cousin next year. Is this correct? And how do i go on to find what x equals which is really 8? please write back sooooon

Hi Irena,

What you have done looks good. The one fact you haven't used is that the product of the ages is 84. That is

which simplifies to

(x - 4)(x - 1)(x - 2) = 168 = 2x2x2x3x7

Since x must be an integer, trial and error is probably the best approach at this point which leads to your solution that x = 8.

Cheers
Harley

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