Date: Mon, 31 May 1999 19:17:39 0600 (CST)
Who is asking: Student
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  x1 
x 
x+1 
oldest  2(x1)2 
2(x1)1 
2(x1) 
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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