Beth and her sisters are going to the state fair. Each ride costs $7, and each exhibit costs $4.

Question

The table shows the number of rides and exhibits each of her sisters rode and viewed.

Rides, r 7 2 5
Exhibits, e 3 5 6

Beth and her sisters each have $65 to spend at the fair. Write an inequality that describes the number of rides and exhibits they each can ride and view.

Answer 1

To create an inequality that describes the amount of money Beth and her sisters can spend at the fair, we can define the variables based on the number of rides and exhibits.

Let:

• \( r \) be the number of rides.
• \( e \) be the number of exhibits.

The cost of each ride is $7, and the cost of each exhibit is $4. Since each person has a budget of $65, we can express the total cost as follows:

\[ 7r + 4e \leq 65 \]

This inequality states that the total cost of the rides and exhibits cannot exceed $65 for each person. Each sister's combination of rides (\( r \)) and exhibits (\( e \)) must satisfy this inequality.

In summary, the inequality that describes the amount of rides and exhibits Beth and her sisters can afford is:

\[ 7r + 4e \leq 65 \]