A charitable organization in Lowell is hosting a black tie benefit. Yesterday, the organization sold 30 regular tickets and 58 VIP tickets, raising $9,346. Today, 26 regular tickets and 59 VIP tickets were sold, bringing in a total of $9,209. How much do the different ticket types cost?
Let's assume the cost of a regular ticket is R and the cost of a VIP ticket is V.
From the information given, we can derive two equations:
30R + 58V = 9346 ...(1)
26R + 59V = 9209 ...(2)
By multiplying equation (2) by 2 and subtracting equation (1), we can eliminate R:
52R + 118V - (30R + 58V) = (52*9209) - (30*9346)
22R + 60V = 479668 - 280380
22R + 60V = 199288 ...(3)
Now, we can solve equations (1) and (3) to find the values of R and V.
By multiplying equation (3) by 3 and subtracting equation (1) multiplied by 10, we can eliminate R once again:
66R + 180V - 10(30R + 58V) = 3(199288) - 10(9346)
66R + 180V = 597864 - 93460
66R + 180V = 504404 ...(4)
Multiplying equation (3) by 3 and subtracting equation (4) multiplied by 1, we can solve for V:
(3)(22R + 60V) - (66R + 180V) = (3)(199288) - 504404
66R + 180V - 66R - 180V = 597864 - 504404
0V = 93460
Since V = 93460/0 is undefined, we cannot determine the exact cost of a VIP ticket.
However, we can find the cost of a regular ticket by substituting V = 0 into equation (3):
22R + 60(0) = 199288
22R = 199288
R = 199288/22
R = 9058.5455
Therefore, the approximate cost of a regular ticket is $9058.55.
Since we cannot determine the exact cost of a VIP ticket, we cannot provide a specific value.