Question

Tanner runs the Tilt-a-whirl ride at the county fair. He charges $2 for kids tickets and $3 for adult tickets. His goal is to make at least $50 each time he runs the ride. The Tilt-a-whirl can only handle a maximum of 3000 pounds. He estimates kids weigh an average of 80 pounds, and adults weigh an average of 200 pounds.

a. Write a system of linear inequalities to represent Tanner's goal of making at least $50 each time he runs the ride.

b. Write a system of linear inequalities to represent the weight limit constraint of the Tilt-a-whirl.

Answer 1

Tanner's goals can be formulated as a system of linear inequalities, with 2x + 3y ≥ 50 representing his earnings goal and 80x + 200y ≤ 3000 representing the weight limit constraint of the Tilt-a-whirl.

Step-by-step explanation:

To represent Tanner's goal of making at least $50 each time he runs the ride, let's denote the number of kids' tickets he sells as x and the number of adult tickets he sells as y. The price for kids' tickets is $2 and for adults is $3. This gives us the inequality:

2x + 3y ≥ 50.

The weight constraint can be represented by another inequality. Considering that the average weight of a kid is 80 pounds and of an adult is 200 pounds, and the Tilt-a-whirl has a maximum weight capacity of 3000 pounds, we have the inequality:

80x + 200y ≤ 3000.

Combining both, we get the system of linear inequalities representing Tanner's goals:

1. 2x + 3y ≥ 50 (Earnings goal)
2. 80x + 200y ≤ 3000 (Weight limit constraint)