Question

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
A) 125, 115
B) 371, -35
C) 81, 146.25
D) 115, 125

Answer 1

To find a viable solution for the number of student and adult tickets that can be sold, we can set up the equation based on the ticket prices and total revenue goal:

Let \( x \) be the number of student tickets sold at $5.00 each, and \( y \) be the number of adult tickets sold at $8.00 each. The equation representing the total revenue from ticket sales is:

\[ 5x + 8y = 1575 \]

Now let's evaluate each of the options provided to see if they satisfy this equation, ensuring that both \( x \) and \( y \) are non-negative integers.

**A) 125 student tickets and 115 adult tickets**
\[ 5(125) + 8(115) = 625 + 920 = 1545 \]
This doesn't meet the total of $1,575.

**B) 371 student tickets and -35 adult tickets**
Student tickets are fine, but adult tickets cannot be negative. Not a viable solution.

**C) 81 student tickets and 146.25 adult tickets**
Adult tickets must be whole numbers. Therefore, 146.25 is not a viable solution.

**D) 115 student tickets and 125 adult tickets**
\[ 5(115) + 8(125) = 575 + 1000 = 1575 \]
This meets the total of $1,575 exactly.

Thus, the only viable solution for the number of student tickets and adult tickets that can be sold is:

**D) 115, 125**