Question

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

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

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

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

A viable solution can include fractional values.

Answer 1

To determine viable solutions for the inequality \( 7x + 4y \geq 400 \), where \( x \) represents the number of adult tickets sold and \( y \) represents the number of children's tickets sold, we need to consider the nature of the variables involved.

1. **Adult tickets and children's tickets are not negative:** You cannot sell a negative number of tickets, and you cannot sell a fraction of a ticket in this context. Therefore, both \( x \) and \( y \) must be non-negative whole numbers.

Given these considerations, the correct response would be:

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