At a concert, 65% of the tickets were sold at full price and 25% of the tickets at half price. The remaining 40 tickets were given away free. The total amount of money collected was $9920. What was the full price of a ticket?

Let's denote the full price of a ticket as X.

1. We know that 65% of the tickets were sold at full price, 25% at half price, and the remaining 10% were given away for free. This is because 65% + 25% = 90%, and 100% - 90% = 10%.

2. We also know that the total number of tickets is 100%, and 10% of the total number of tickets is 40 (the number of free tickets). Therefore, the total number of tickets is 40 / 10% = 400 tickets.

3. Now, we know that 65% of the tickets were sold at full price, which is 65% * 400 = 260 tickets.

4. Similarly, 25% of the tickets were sold at half price, which is 25% * 400 = 100 tickets.

5. The total amount of money collected was $9920. This amount comes from the full price tickets and the half price tickets. Therefore, we can set up the following equation: 260X + 100 * 0.5X =$9920.

6. Simplifying the equation gives us 260X + 50X = $9920, or 310X =$9920.

7. Solving for X, we get X = $9920 / 310 =$32.

Therefore, the full price of a ticket was $32.