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?

a. (115,125)
b. (81,146.25)
c. (125,115)
d. (371,−35)

Answer 1

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.