The entry tickets for a local fair cost $7 for adults and $4 for children. In order for the fairgrounds to earn a profit, they must make at least $400. If this situation is modeled by the inequality 7x+4y≥400

Question

, which of the following constraints should be used to determine viable solutions?(1 point)
Responses

A viable solution can include fractional values.
A viable solution can include fractional values.

A viable solution will have only positive whole numbers.
A viable solution will have only positive whole numbers.

A viable solution can have positive or negative numbers.
A viable solution can have positive or negative numbers.

There is only one viable solution.
There is only one viable solution.

Answer 1

In the context of the ticket sales for the fair, the variables \( x \) and \( y \) represent the number of adult tickets and children's tickets sold, respectively. Since you cannot sell a fraction of a ticket and negative ticket sales do not make sense, the most appropriate constraint for viable solutions is:

A viable solution will have only positive whole numbers.

This means both \( x \) and \( y \) must be non-negative integers (whole numbers equal to or greater than zero).