Question

Threads Garage is a thrift store that sells clothing by the pound. Customers fill a plastic bag with their desired amount of clothing. Then, the bag is then weighed at checkout to calculate the cost. There is a linear relationship between the weight of a bag of clothing, in pounds, and its cost. 3 6 9 12 15 18 21 24 $3 $6 $9 $12 $15 $18 $21 $24 x y Weight (pounds) Cost ($) Describe the rate of change for this relationship. The cost of a bag of clothing increases decreases by $0.40 $0.50 $2.00 $2.50 $3.00 $9.00 per pound.

Answer 1

To determine the rate of change for the relationship between weight (in pounds) and cost (in dollars), we can examine the values provided.

From the data:

• For 3 pounds, the cost is $3.
• For 6 pounds, the cost is $6.
• For 9 pounds, the cost is $9.
• For 12 pounds, the cost is $12.
• For 15 pounds, the cost is $15.
• For 18 pounds, the cost is $18.
• For 21 pounds, the cost is $21.
• For 24 pounds, the cost is $24.

The cost increases in increments of $3 for each increment of 3 pounds. Therefore, for every additional pound, the cost increases by:

\[ \text{Rate of Change} = \frac{\text{Change in Cost}}{\text{Change in Weight}} = \frac{3}{3} = 1 \]

Thus, the cost of a bag of clothing increases by $1.00 per pound.

Given the options listed in your question, it looks like there might be an error in the options. The closest equivalent rate of change, calculated based on the data, shows that the cost increases by $1.00 per pound, which is not listed. However, we can conclude that:

• The cost of a bag of clothing increases by $1.00 per pound.