A venue sold 8000 tickets for a concert. VIP tickets cost 50 and popular stand tickets cost 30. If the total revenue was $250,000, how many of each type of ticket were sold?

Let $V$ be the number of VIP tickets sold and $P$ be the number of popular stand tickets sold.
Given:

• Total number of people: 8000
• Price of VIP ticket: \50$
• Price of popular stand ticket: \30$
• Total revenue: \250,000$

From this, we form two equations:

$$V + P = 8000 \quad (1)$$ $$50V + 30P = 250000 \quad (2)$$

Subtract $V$ from both sides of equation (1):

$$P = 8000 - V$$

Substitute $P = 8000 - V$ into equation (2):

$$50V + 30(8000 - V) = 250000$$

Distribute the 30:

$$50V + 240000 - 30V = 250000$$

Combine like terms ($50V - 30V$):

$$20V + 240000 = 250000$$

Subtract 240000 from both sides:

$$20V = 250000 - 240000$$ $$20V = 10000$$

Divide by 20:

$$V = \frac{10000}{20}$$ $$V = 500$$

Using $P = 8000 - V$:

$$P = 8000 - 500$$ $$P = 7500$$

The number of VIP tickets sold is 500 and the number of popular stand tickets sold is 7500.

$$V = 500, P = 7500$$