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?

Question

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.