Question

Tell whether the relationship in following problem represents a direct or inverse proportion. Explain your answer.

The music director at a school wants students to sell 200 tickets to the spring musical. The 200 tickets are distributed to the students in equal amounts so that each student gets y tickets to sell. The number of tickets each student gets is given by the equation y = 200/x

Answer 1

The relationship given by y = 200/x is an inverse proportion because as the number of students x increases, the number of tickets y decreases, and the product xy remains constant.

Step-by-step explanation:

The relationship in the given problem, where the number of tickets y each student gets is given by the equation y = 200/x, represents an inverse proportion.

In this situation, as the number of students (x) increases, the number of tickets each student is responsible for selling (y) decreases. This is because the total number of tickets to be sold is fixed at 200. The relationship is an example of an inverse proportion because when one variable goes up, the other goes down, and the product of the two variables remains a constant (y * x = 200 in this case).

If we were to plot this relationship, it would result in a curve that approaches the axes but never intersects them. This is characteristic of an inverse proportional relationship. In contrast, a direct proportional relationship is represented by a straight line through the origin when plotted on a graph.