Bot GPT 4-o mini To determine the equation that represents the total charge in dollars (y) for a delivery of x cookies, we can analyze the information provided.
Given Information:
- The bakery charges a $5 delivery fee.
- The cost for delivering:
- 12 cookies is $20
- 18 cookies is $27.50
From the above, we can identify the total cost, which includes the delivery fee and the cost of the cookies themselves.
Step 1: Calculate Cost of Cookies
For 12 cookies:
Total charge = $20
Delivery fee = $5
Cost of cookies = Total charge - Delivery fee
Cost of cookies = $20 - $5 = $15
Cost per cookie = $15 / 12 = $1.25
For 18 cookies:
Total charge = $27.50
Delivery fee = $5
Cost of cookies = Total charge - Delivery fee
Cost of cookies = $27.50 - $5 = $22.50
Cost per cookie = $22.50 / 18 = $1.25
Step 2: Generalize the Information
From both cases, we can see that the cost per cookie is consistent at $1.25. Therefore, we can express the total charge (y) as a function of the number of cookies (x):
Step 3: Formulating the Equation
The total charge y for x cookies can be represented as: \[ y = 1.25x + 5 \] where:
- 1.25 is the cost per cookie,
- 5 is the delivery fee.
Step 4: Create Data Table
To verify, we can create a simple table with the values:
| Cookies (x) | Total Charge (y) | |-------------|-------------------| | 12 | 20 | | 18 | 27.50 | | 0 | 5 | (representing just the delivery fee)
Using the equation \(y = 1.25x + 5\):
- For \(x = 12\): \(y = 1.25(12) + 5 = 15 + 5 = 20\) (correct)
- For \(x = 18\): \(y = 1.25(18) + 5 = 22.5 + 5 = 27.50\) (correct)
Conclusion:
The equation representing the total charge in dollars, \(y\), for a delivery of \(x\) cookies is: \[ y = 1.25x + 5 \]
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