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

(81,146.25)
left parenthesis 81 comma 146.25 right parenthesis

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

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

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

Answer 1

To determine which of the given pairs \((x, y)\) (where \(x\) is the number of student tickets and \(y\) is the number of adult tickets) is a viable solution for raising a total of $1,575.00, we can use the equation:

\[ 5x + 8y = 1575 \]

Now let's evaluate each of the provided pairs.

1. **(81, 146.25)**:
\[ 5(81) + 8(146.25) = 405 + 1170 = 1575 \]
This works, but \(y\) needs to be a whole number since you can't sell a fraction of a ticket.

2. **(371, -35)**:
\[ 5(371) + 8(-35) = 1855 - 280 = 1575 \]
This works mathematically, but selling a negative number of tickets for adults is not viable.

3. **(125, 115)**:
\[ 5(125) + 8(115) = 625 + 920 = 1545 \]
This does not reach the total goal of 1575.

4. **(115, 125)**:
\[ 5(115) + 8(125) = 575 + 1000 = 1575 \]
This works perfectly.

The only viable solutions that meet the conditions of the problem are:

- \( (115, 125) \)

So the viable solution is **(115, 125)**.