admission tickets to an advanced movie screening were priced at P 200 for adult and P 150 for students. If 450 tickets were sold and the total receipts were P 14, 400. How many of each type of tickets were sold?
200x + 150(450-x) = 14400
solve for x
To solve this problem, let's use a system of equations.
Let's represent the number of adult tickets sold as 'A' and the number of student tickets sold as 'S.'
Given the following information:
- Admission price for an adult ticket is P200.
- Admission price for a student ticket is P150.
- Total number of tickets sold is 450.
- Total receipts from the sales of tickets are P14,400.
We can set up the following equations:
1) A + S = 450 (Equation 1 represents the total number of tickets sold, which is 450.)
2) 200A + 150S = 14,400 (Equation 2 represents the total receipts, which is P14,400.)
Now we can solve this system of equations.
There are multiple ways to solve a system of equations, but here's one method:
1) Solve Equation 1 for A in terms of S:
A = 450 - S
2) Substitute this value of A into Equation 2 and solve for S:
200(450 - S) + 150S = 14,400
90,000 - 200S + 150S = 14,400
-50S = -75,600
S = 1,512
3) Substitute the value of S back into Equation 1 to solve for A:
A + 1,512 = 450
A = -1,062
However, since we can't have negative ticket sales, there must be an error in the calculations. Please double-check the values given in the question, as they might be incorrect.