Question

Brad is distributing Halloween candy. He hopes that there will be some left over for him when all the trick-or-treaters are done!

There is a linear relationship between the number of trick-or-treaters that have visited the house and the pieces of candy left.

Number of trick-or-treaters

Pieces of candy left

0

15

30

45

150

105

60

15

Describe the rate of change for this relationship.

The amount of candy left

by

per trick-or-treater.

Answer 1

To determine the rate of change for the relationship between the number of trick-or-treaters and the pieces of candy left, we can observe the data provided:

- When there are 0 trick-or-treaters, there are 15 pieces of candy left.
- When there are 30 trick-or-treaters, there are 45 pieces of candy left.
- When there are 150 trick-or-treaters, there are 105 pieces of candy left.
- When there are 60 trick-or-treaters, there are 15 pieces of candy left.

We can calculate the change in the number of trick-or-treaters and the change in the pieces of candy left for these points.

Let's analyze the two specific points that will help us find the rate of change:

1. From 0 to 30 trick-or-treaters:
- Change in trick-or-treaters = 30 - 0 = 30
- Change in candy left = 45 - 15 = 30
- Rate of change = Change in candy left / Change in trick-or-treaters = 30 / 30 = 1 piece of candy left per trick-or-treater.

2. From 30 to 150 trick-or-treaters:
- Change in trick-or-treaters = 150 - 30 = 120
- Change in candy left = 105 - 45 = 60
- Rate of change = Change in candy left / Change in trick-or-treaters = 60 / 120 = 0.5 pieces of candy left per trick-or-treaters.

These calculations suggest that as the number of trick-or-treaters increases, the pieces of candy left decreases at a changing rate.

In summary, the rate of change can vary depending on the increments of trick-or-treaters examined. However, in general terms:

**The amount of candy left decreases by an average of around** 1 piece **per trick-or-treater at lower numbers of trick-or-treaters, and about** 0.5 pieces **per trick-or-treater as it approaches 150 trick-or-treaters.**

In conclusion, the relationship shows a decreasing trend, where Brad loses candy as more trick-or-treaters come to his house.