To determine which option is a viable solution for the number of student and adult tickets sold that meets the fundraising goal of $1,575.00, we can use the equation derived from the ticket prices and the total goal.
Let \( x \) be the number of student tickets sold and \( y \) be the number of adult tickets sold. The total revenue can be represented by the equation:
\[ 5x + 8y = 1575 \]
Now let's evaluate each option.
Option a: (115, 125)
- Calculate the total revenue: \[ 5(115) + 8(125) = 575 + 1000 = 1575 \]
- This satisfies the equation.
Option b: (81, 146.25)
- Since \( y \) needs to be a whole number, 146.25 is not a viable count for adult tickets. Therefore, this option is not valid.
Option c: (125, 115)
- Calculate the total revenue: \[ 5(125) + 8(115) = 625 + 920 = 1545 \]
- This does not satisfy the equation.
Option d: (371, -35)
- Since \( y \) needs to be a non-negative whole number, -35 is not valid. Therefore, this option is also not viable.
The only viable option from the provided solutions is:
a. (115, 125)
This combination meets the fundraising goal.