Question

Barbara wants to buy carpeting for her new home. She will need different sized carpets in each room. There is a linear relationship between the size of a carpet, in square feet, and its cost. 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 $100 $200 $300 $400 $500 $600 $700 $800 $900 $1,000 $1,100 $1,200 $1,300 $1,400 $1,500 x y Carpet size (square feet) Cost ($) Describe the rate of change for this relationship. The cost of a carpet increases decreases by $0.20 $1.50 $8.33 $10.00 $150.00 $200.00 per square foot.

Answer 1

To determine the rate of change for the relationship between the size of the carpet (in square feet) and its cost (in dollars), we can analyze the data you provided.

From the given points:

- At 20 square feet, the cost is $100.
- At 100 square feet, the cost is $500.
- At 200 square feet, the cost is $1,000.

Let's calculate the rate of change, which can be defined as the change in cost divided by the change in square footage.

1. Calculate the change in cost between two points:
- From 20 to 100 square feet:
- Change in cost = $500 - $100 = $400
- Change in square feet = 100 - 20 = 80

The rate of change (slope) = Change in cost / Change in square feet = $400 / 80 = $5.00 per square foot.

2. Check another interval for verification:
- From 100 to 200 square feet:
- Change in cost = $1,000 - $500 = $500
- Change in square feet = 200 - 100 = 100

The rate of change (slope) = Change in cost / Change in square feet = $500 / 100 = $5.00 per square foot.

Since the calculation is consistent across the intervals, we can conclude that the cost of carpeting increases by **$5.00 per square foot**.

So, the answer would be:
The cost of a carpet increases by **$5.00 per square foot**.