VIP to General Admission Ticket Price Ratio

During a charity event, the organizers sold tickets for two different types of seating: VIP and General Admission. The ratio of VIP tickets sold to General Admission tickets sold was 3:5. After the event, they discovered that the total revenue generated from the VIP ticket sales was $9,000 and from the General Admission ticket sales was $10,500.

Let the number of VIP tickets sold be represented as $V$ and the number of General Admission tickets sold be represented as $G$. If the price of a VIP ticket was $P_{VIP}$ and the price of a General Admission ticket was $P_{GA}$, we can write the following equations based on the problem description:

1. The ratio relationship gives us: $\frac{V}{G} = \frac{3}{5}$

2. The revenue equations are: $V \cdot P_{VIP} = 9000$ and $G \cdot P_{GA} = 10500$.

Determine the value of $\frac{P_{VIP}}{P_{GA}}$ (the price of a VIP ticket relative to the price of a General Admission ticket, expressed as a fraction). Enter your answer in the grid below as an irreducible fraction.