Two friends, Mia and Zara, are discussing a mixture of two types of fruit juices. Mia's juice has $2$ parts of apple juice for every $3$ parts of orange juice, while Zara's juice has $3$ parts of apple juice for every $2$ parts of orange juice. They decide to mix their juices in a new ratio for a party. Their new mixture consists of $4$ parts of Mia's juice for every $5$ parts of Zara's juice. Determine the ratio of apple juice to orange juice in the final mixture of their combined juices.