Question

Atticus loves to eat bagels to fuel up for his track meets. He typically buys them fresh from the bakery.
There is a linear relationship between the number of bagels Atticus buys and the total cost.
Number of bagels Total cost
2 $2.50
4 $5.00
6 $7.50
8 $10.00
Describe the rate of change for this relationship.
The total cost
by
per bagel.

Answer 1

To determine the rate of change for the relationship between the number of bagels and the total cost, we can look at the provided data points.

We see that:
- For 2 bagels, the total cost is $2.50.
- For 4 bagels, the total cost is $5.00.
- For 6 bagels, the total cost is $7.50.
- For 8 bagels, the total cost is $10.00.

The total cost increases by $2.50 when the number of bagels increases by 2.

To find the rate of change (the cost per bagel), we can calculate it as follows:

1. **Change in Total Cost**: The change in cost from 2 bagels to 4 bagels is:
\[
5.00 - 2.50 = 2.50 \text{ dollars}
\]

2. **Change in Number of Bagels**: The change in the number of bagels from 2 to 4 is:
\[
4 - 2 = 2 \text{ bagels}
\]

3. **Rate of Change**: Now, divide the change in cost by the change in the number of bagels to find the cost per bagel:
\[
\text{Rate of change} = \frac{\text{Change in Total Cost}}{\text{Change in Number of Bagels}} = \frac{2.50}{2} = 1.25 \text{ dollars per bagel}
\]

Thus, the total cost **increases by $1.25 per bagel**.