The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 45 balcony tickets and 42 general admission floor tickets for Friday's show, for a total of $3,087 in receipts. For Saturday's show, 26 balcony tickets and 76 general admission floor tickets have been sold, equaling $2,870 in receipts. How much does a balcony seat ticket cost and how much does a general admission floor ticket?
Let's assume the cost of a balcony ticket is B and the cost of a general admission floor ticket is G.
For Friday's show:
45 balcony tickets were sold at $B each, totaling 45*B dollars.
42 general admission floor tickets were sold at $G each, totaling 42*G dollars.
The total receipts for Friday's show are 45*B + 42*G = $3,087.
For Saturday's show:
26 balcony tickets were sold at $B each, totaling 26*B dollars.
76 general admission floor tickets were sold at $G each, totaling 76*G dollars.
The total receipts for Saturday's show are 26*B + 76*G = $2,870.
To solve the system of equations, we can set up the following equations:
45B + 42G = 3,087 ...(1)
26B + 76G = 2,870 ...(2)
To eliminate B, we can multiply equation (1) by 26 and equation (2) by 45:
1,170B + 1,092G = 80,262 ...(3)
1,170B + 3,420G = 128,850 ...(4)
Subtracting equation (3) from equation (4) will eliminate B:
1,170B + 3,420G - (1,170B + 1,092G) = 128,850 - 80,262
2,328G = 48,588
Simplifying the equation:
G = 48,588 / 2,328
G = 20.89 (approximately)
Substituting the value of G back into equation (1):
45B + 42 * 20.89 = 3,087
45B + 878.38 = 3,087
45B = 3,087 - 878.38
45B = 2,208.62
Simplifying and finding the value of B:
B = 2,208.62 / 45
B = 49.19 (approximately)
Therefore, the cost of a balcony seat ticket is approximately $49.19 and the cost of a general admission floor ticket is approximately $20.89.