To determine if the given options represent viable solutions for the number of student and adult tickets that can be sold, we can set up the equation based on the total amount raised:
The equation for total revenue from ticket sales can be expressed as:
\(5x + 8y = 1575\)
where \(x\) is the number of student tickets, and \(y\) is the number of adult tickets.
Let's evaluate each option:
-
(81, 146.25):
- This represents 81 student tickets and 146.25 adult tickets. Since the number of tickets must be whole numbers, this cannot be a valid solution.
-
(125, 115):
- Substitute \(x = 125\) and \(y = 115\): \[ 5(125) + 8(115) = 625 + 920 = 1545 \]
- This totals $1545, which is less than $1575. So, this is not a solution.
-
(115, 125):
- Substitute \(x = 115\) and \(y = 125\): \[ 5(115) + 8(125) = 575 + 1000 = 1575 \]
- This totals $1575, which matches the goal. This is a valid solution.
-
(371, -35):
- This represents 371 student tickets and -35 adult tickets. Tickets cannot be sold in negative quantities, so this cannot be a valid solution.
Summary of potential solutions:
- (81, 146.25) - Not a viable solution (non-integer tickets).
- (125, 115) - Not a viable solution (total too low).
- (115, 125) - Viable solution (total matches $1575).
- (371, -35) - Not a viable solution (negative tickets).
The only viable solution is (115, 125).