Three different stores are having a sale on sweatshirts. The tables show the number of sweatshirts and the price of the sweatshirts for each store.

Question

To determine if the cost per sweatshirt is the same for each of the number of sweatshirts purchased, you can check for a constant of proportionality. Start by finding the cost per sweatshirt when you purchase 8 sweatshirts.

Number of sweatshirts Cost in dollars Cost per sweatshirt
8 25

2 7
5 16

Answer 1

To find the cost per sweatshirt when purchasing 8 sweatshirts from the first store, we can calculate it as follows:

1. Calculate the cost per sweatshirt for 8 sweatshirts: \[ \text{Cost per sweatshirt} = \frac{\text{Total cost}}{\text{Number of sweatshirts}} = \frac{25}{8} \] \[ \frac{25}{8} = 3.125 \]

So, the cost per sweatshirt for 8 sweatshirts is $3.125.

Next, let's calculate the cost per sweatshirt for the other two stores.

2. For the second store (2 sweatshirts for $7): \[ \text{Cost per sweatshirt} = \frac{\text{Total cost}}{\text{Number of sweatshirts}} = \frac{7}{2} \] \[ \frac{7}{2} = 3.5 \]

3. For the third store (5 sweatshirts for $16): \[ \text{Cost per sweatshirt} = \frac{\text{Total cost}}{\text{Number of sweatshirts}} = \frac{16}{5} \] \[ \frac{16}{5} = 3.2 \]

Now, we summarize the cost per sweatshirt for all three stores:

• Store 1 (8 sweatshirts for $25): $3.125
• Store 2 (2 sweatshirts for $7): $3.50
• Store 3 (5 sweatshirts for $16): $3.20

Since the cost per sweatshirt is not the same for each store, there is no constant of proportionality among these prices.