Let

x = the number of $10 tickets sold

y = the number of $20 tickets sold

z = the number of $30 VIP tickets sold

The team has sold 3450 tickets overall means:

x + y + z = 3450

It sold 190 more $20 tickets than $10 tickets means:

y = 190 + x

The total sales are $67,310 means:

10x + 20y + 30z = 67310 divide both sides by 10

x + 2y + 3z = 6731

Now we have the following system of equations:

x + y + z = 3450

y = 190 + x

x + 2y + 3z = 6731

........

Click here to see the step by step solution for x , y and z

........

x = 1,143 $10 tickets

y = 1,333 $20 tickets

z = 974 VIP tickets

There were 1,143 $10 tickets, 1,333 $20 tickets and 974 VIP tickets sold.