To determine which option is a viable solution for the number of student and adult tickets sold, we can set up the following equation based on the total revenue generated from ticket sales:
Let:
- \( x \) = number of student tickets sold at $5 each
- \( y \) = number of adult tickets sold at $8 each
The equation to represent the total amount raised is:
\[ 5x + 8y = 1575 \]
Now we will evaluate each option provided:
-
(125, 115) \[ 5(125) + 8(115) = 625 + 920 = 1545 \quad (\text{not } 1575) \]
-
(115, 125) \[ 5(115) + 8(125) = 575 + 1000 = 1575 \quad (\text{valid solution}) \]
-
(371, -35) \[ 5(371) + 8(-35) = 1855 - 280 = 1575 \quad (\text{but } -35 \text{ tickets is not possible}) \]
-
(81, 146.25) \[ 5(81) + 8(146.25) = 405 + 1170 = 1575 \quad (\text{but } 146.25 \text{ tickets is not possible}) \]
From the calculations, the only viable solution that results in a valid number of tickets is:
(115, 125)
This means selling 115 student tickets and 125 adult tickets successfully meets the target of raising $1,575.