Question

yesterday the organization sold 69 regular tickets and 96 VIP tickets raising $19,995 today 46 regular tickets and 32 VIP tickets were sold bringing in a total of $8,114 how much do the different ticket types cost?​

Answer 1

Explanation:

Let's denote the cost of a regular ticket as "R" and the cost of a VIP ticket as "V". We can then set up a system of equations based on the information given in the problem:

69R + 96V = 19995 (yesterday's sales)

46R + 32V = 8114 (today's sales)

We can solve for one of the variables in terms of the other by using the second equation. First, let's simplify it by dividing both sides by 2:

23R + 16V = 4057

Now we can solve for one variable in terms of the other. Let's solve for V:

16V = 4057 - 23R

V = (4057 - 23R)/16

We can substitute this expression for V into the first equation and solve for R:

69R + 96[(4057 - 23R)/16] = 19995

Multiplying both sides by 16 to eliminate the fraction:

1104R + 96(4057 - 23R) = 319920

Distributing the multiplication:

1104R + 389232 - 2208R = 319920

Simplifying and solving for R:

-1104R = -69312

R = 63

Now that we know that a regular ticket costs $63, we can substitute this value into the expression we derived for V:

V = (4057 - 23R)/16 = (4057 - 23(63))/16 = 267

Therefore, a VIP ticket costs $267.