2. Goran had three times as many years as Violet had when he was her current age. Determine the ratio of Goran's age to Violet's age.
Solution. Let Goran now be $x$ years old, and Violeta $y$ years old. When Goran was at her-

![](https://cdn.mathpix.com/cropped/2024_06_05_80dc60fa593a90b95c1cg-1.jpg?height=125&width=586&top_left_y=1230&top_left_x=858)
current age, he was $x-(x-y)$ years old, and she was $y-(x-y)$ years old. Therefore,

$$
x-(x-y)=3(y-(x-y))
$$

which means $3 x=5 y$. We conclude that the ratio of Goran's age to Violeta's age is 5:3.