Problem of the week #45 - February 4th, 2013

[Jameson]

The present age of Adam is three times that of his son. Six years ago, the age of Adam was four times that of his son. Find the ratio of their ages 6 years later.
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[Jameson]

Congratulations to the following members for their correct solutions:

1) Sudharaka
2) Reckoner

Solution (from Reckoner):

Spoiler

Call Adam's age \(x\) and his son's age \(y\). The given information is summarized by these equations:
\[\left\{\begin{array}{rcl}x &=& 3y\\ x-6 &=& 4(y-6)\end{array}\right.\]\[\Rightarrow\left\{\begin{array}{rcl}x - 3y &=& 0\\ x-4y &=&-18\end{array}\right.\]
Solving this system, we find that \(x=54\) and \(y=18\), their current age. Therefore, in six years, Adam will be 60 and his son will be 24, so that the ratio of their ages will be \(\frac52\).