Question

Review #3
A bakery delivers cookies to offices.



*The bakery charges a $5 delivery fee.

*The bakery charges a total of $20 for delivering 12 cookies

*The bakery charges a total of $27.50 for delivering 18 cookies



Which equation represents the total charge in dollars, y, for a delivery of x cookies?

Hint: Can we create a table to enter into our Desmos calcuator to help us?

Remember to put y1 ~ mx1 + b in the second entry to see the slope and y-intercept.

Answer 1

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:
1. The bakery charges a $5 delivery fee.
2. 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:
\[
y = 1.25x + 5
\]