Question

Vivian plans to make beaded keychains to give out to her friends as party favors. She purchases a large bag of colorful beads and begins assembling the keychains.
There is a linear relationship between the number of keychains Vivian makes, and the number of beads left in the bag.
some of the main points are (0,500) (2,450) (6,350) (8,300) and so on
Describe the rate of change for this relationship.
The number of beads left in the bag decreases by ___ per keychain.

Answer 1

To determine the rate of change for the relationship between the number of keychains Vivian makes and the number of beads left in the bag, we can look at the points provided:

- (0, 500)
- (2, 450)
- (6, 350)
- (8, 300)

Let's analyze the data to find the rate of change:

1. From (0, 500) to (2, 450):
- Change in keychains: \(2 - 0 = 2\)
- Change in beads: \(450 - 500 = -50\)
- Rate of change: \(\frac{-50}{2} = -25\)

2. From (2, 450) to (6, 350):
- Change in keychains: \(6 - 2 = 4\)
- Change in beads: \(350 - 450 = -100\)
- Rate of change: \(\frac{-100}{4} = -25\)

3. From (6, 350) to (8, 300):
- Change in keychains: \(8 - 6 = 2\)
- Change in beads: \(300 - 350 = -50\)
- Rate of change: \(\frac{-50}{2} = -25\)

The calculations consistently show that for each keychain Vivian makes, the number of beads left in the bag decreases by 25.

Thus, the number of beads left in the bag decreases by **25** per keychain.