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

Status
Not open for further replies.

#### Jameson

Staff member
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.
--------------------
Remember to read the POTW submission guidelines to find out how to submit your answers!

#### Jameson

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$$.