Problem C

Coin Collection

Arya has never travelled to another country, but has a collection of foreign coins given to him by friends and family who have. In his collection he has \(10\) coins from Africa, \(6\) coins from Asia, \(7\) coins from South America, and \(8\) coins from Europe.

One day Arya’s grandfather added some Australian coins to the collection. After he did that, he told Arya that if he took a coin at random from the collection, the probability of it being from either Africa or Asia was \(\frac{4}{9}\).

How many Australian coins did Arya’s grandfather add to the collection?

**Theme(s):** Data Management