To raise money, the student council at a local middle school is hosting a talent show. Tickets are sold for $5.00 for students (x) and $8.00 for adults (y). The goal is to raise a total of $1,575.00. Which of the following is a viable solution for the number of student and adult tickets that can be sold?(1 point)

Responses

(125,115)
left parenthesis 125 comma 115 right parenthesis

(115,125)
left parenthesis 115 comma 125 right parenthesis

(371,−35)
left parenthesis negative 371 comma negative 35 right parenthesis

(81,146.25)

1 answer

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:

  1. (125, 115) \[ 5(125) + 8(115) = 625 + 920 = 1545 \quad (\text{not } 1575) \]

  2. (115, 125) \[ 5(115) + 8(125) = 575 + 1000 = 1575 \quad (\text{valid solution}) \]

  3. (371, -35) \[ 5(371) + 8(-35) = 1855 - 280 = 1575 \quad (\text{but } -35 \text{ tickets is not possible}) \]

  4. (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.