Yesterday, the organization sold 69 regular tickets and 40 vip tickets, raising $12,601. today, 80 regular tickets and 55 vip tickets were sold, bringing in a total of $16,300. how much do the different ticket types cost?

Write the equation based on the problem
r stands for the price of a regular ticket, v stands for the price of a VIP ticket.
⇒ 69r + 40v = 12,601
⇒ 80r + 55v = 16,300

Solve  the equation using elimination method.
I'm eliminating v, so I can find the r. We can eliminate v by changing the coefficient of first and second equation into the same number.
69r + 40v = 12,601 (multiply 11)
80r + 55v = 16,300 (multiply 8)

759r + 440v = 138,611
640r + 440v = 130,400
- (substract)
119r             = 8,211
     r             = 69

Subtitute 69 as r to one of the equation and find v
80r + 55v = 16,300
80(69) + 55v = 16,300
5,520 + 55v = 16,300
55v = 10,780
v = 196

So the price of a regular ticket is $69 and the price of a VIP ticket is $196

Find the difference
difference = 196 - 69
difference = 127

The difference is $127