<PRE><B>Question 1203174</B>
&lt;pre&gt;
Six years ago, Lydia was three times as old as Keiko. In three years time, Lydia will be twice as old as Keiko. What are their present ages?

Let Lydia and Keiko&#39;s ages be L and K, respectively
Then we get L - 6 = 3(K - 6)____L - 6 = 3K - 18___L - 3K = - 12 ----- eq (i)
Also, L + 3 = 2(K + 3)_____L + 3 = 2K + 6_____L - 2K = 3 ----- eq(ii)
Subtracting eq (i) from eq (ii), we find that &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;Keiko&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, or K = 12 + 3 = &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;15 years-old&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;

Substituting 15 for K in eq (ii), we get: L - 2(15) = 3 
                                             L - 30 = 3
                                       &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;Lydia&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, or L = 3 + 30 = &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;33 years-old&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/pre&gt;</PRE>