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

Question

To determine if the cost per plate is the same for each of the number of plates purchased, you can check for a constant of proportionality. Start by finding the cost per plate when you purchase 5 plates.

Number of plates Cost in dollars Cost per plate
5 23

8 32
10 38

Answer 1

To find the cost per plate for purchasing 5 plates, we'll need to divide the total cost by the number of plates.

From the table given:

• For 5 plates, the cost is $23.

Now, we calculate the cost per plate:

\[ \text{Cost per plate} = \frac{\text{Total cost}}{\text{Number of plates}} = \frac{23}{5} = 4.6 \]

So, the cost per plate when purchasing 5 plates is $4.60.

Let's also calculate the cost per plate for the other quantities of plates in the table:

1. For 8 plates: \[ \text{Cost per plate} = \frac{32}{8} = 4.0 \]

2. For 10 plates: \[ \text{Cost per plate} = \frac{38}{10} = 3.8 \]

Now we summarize the cost per plate for each quantity:

• 5 plates: $4.60
• 8 plates: $4.00
• 10 plates: $3.80

The cost per plate is different for each quantity of plates, indicating that the cost does not have a constant proportionality across the different amounts purchased.