THERE WERE 390 ADULT AND CHILDREN TICKETS THAT WERE SOLD AT A PLAY. THE THEATRE SOLD 2.25 TIMES MORE ADULT TICKETS THEN CHILDREN TICKETS. IF ADULT TICKETS COST $8 AND CHILD TICKETS COST $3. WHAT WAS THE TOTAL REVENUE FOR THE AMOUNT OF TICKETS SOLD?

To find the total revenue from the ticket sales, we first need to determine the number of adult and children tickets sold.

Let's represent the number of children tickets as 'x'. Since the theater sold 2.25 times more adult tickets than children tickets, the number of adult tickets sold would be 2.25x.

The problem states that a total of 390 adult and children tickets were sold, so we can create an equation based on this information:

x + 2.25x = 390

Combining like terms, we have:
3.25x = 390

Now, we can solve for the value of x by dividing both sides of the equation by 3.25:
x = 390 / 3.25
x = 120

Therefore, 120 children tickets were sold. To find the number of adult tickets sold, we can substitute this value back into our equation:
2.25x = 2.25 * 120
2.25x = 270

So, 270 adult tickets were sold.

Now, we can calculate the total revenue by multiplying the number of children tickets by the ticket price for children ($3) and the number of adult tickets by the ticket price for adults ($8), then adding the two amounts:

Revenue = (Number of children tickets * Price per child ticket) + (Number of adult tickets * Price per adult ticket)
Revenue = (120 * $3) + (270 * $8)
Revenue = $360 + $2160
Revenue = $2520

Therefore, the total revenue from the ticket sales is $2520.