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.

Question

There is a linear relationship between the weight of a bag of clothing, in pounds, and its cost.

Weight (pounds)

Cost

3

$9.00

6

$15.00

9

$21.00

12

$27.00

Describe the rate of change for this relationship.

The cost of a bag of clothing

by

per pound.

Answer 1

To determine the rate of change for the relationship between the weight of a bag of clothing and its cost, we can analyze the data provided.

From the given information:

• At 3 pounds, the cost is $9.00.
• At 6 pounds, the cost is $15.00.
• At 9 pounds, the cost is $21.00.
• At 12 pounds, the cost is $27.00.

We can calculate the cost per pound by finding the difference in cost for a specific increase in weight:

1. From 3 pounds to 6 pounds: \[ \text{Cost change} = 15 - 9 = 6 \quad(\text{dollars}) \] \[ \text{Weight change} = 6 - 3 = 3 \quad(\text{pounds}) \] \[ \text{Cost per pound} = \frac{6}{3} = 2 \quad(\text{dollars per pound}) \]

2. From 6 pounds to 9 pounds: \[ \text{Cost change} = 21 - 15 = 6 \quad(\text{dollars}) \] \[ \text{Weight change} = 9 - 6 = 3 \quad(\text{pounds}) \] \[ \text{Cost per pound} = \frac{6}{3} = 2 \quad(\text{dollars per pound}) \]

3. From 9 pounds to 12 pounds: \[ \text{Cost change} = 27 - 21 = 6 \quad(\text{dollars}) \] \[ \text{Weight change} = 12 - 9 = 3 \quad(\text{pounds}) \] \[ \text{Cost per pound} = \frac{6}{3} = 2 \quad(\text{dollars per pound}) \]

In each case, the cost increases by $6 for every 3 pounds. Therefore, the rate of change can be consistently expressed as $2.00 per pound.

So, the cost of a bag of clothing increases by $2.00 per pound.