Question

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?

y = 1.25x + 5

y = 5x + 1.25

y = 1.25x + 6

y= 5x + 7.50
Answer
you sure
Answered by GPT-4o mini
To find the equation that represents the total charge in dollars, \( y \), for a delivery of \( x \) cookies, we can start by analyzing the information given.

1. **Delivery Fee**: The bakery charges a flat delivery fee of $5. This means that the cost of cookies will be added to this fee.

2. **Cost of Cookies**: We can find the cost per cookie by looking at the total costs given:

- For 12 cookies, the total charge is $20, which includes the $5 delivery fee. Thus, the cost for the cookies alone is:
\[
20 - 5 = 15 \text{ (for 12 cookies)}
\]
The cost per cookie is:
\[
\frac{15}{12} = 1.25
\]

- For 18 cookies, the total charge is $27.50, which also includes the $5 delivery fee. The cost for the cookies in this case is:
\[
27.50 - 5 = 22.50 \text{ (for 18 cookies)}
\]
The cost per cookie is:
\[
\frac{22.50}{18} = 1.25
\]

From the above calculations, we can determine that the cost per cookie is $1.25.

Putting it all together, the total cost \( y \) for \( x \) cookies can be represented by the equation:
\[
y = 1.25x + 5
\]

Thus, the correct equation is:
\[
\boxed{y = 1.25x + 5}
\]
Answered by GPT-4o mini
Yes, I am confident in the calculations. Let's go through the problem step by step once more to confirm the correctness.

1. **Understanding the Charges**:
- The bakery has a delivery fee of **$5**.
- The cost of cookies needs to be determined based on the examples given.

2. **Calculating Costs from Examples**:
- When delivering **12 cookies**, the total charge is **$20**. Therefore, the cost of the cookies is:
\[
\text{Cost of cookies} = 20 - 5 = 15
\]
Since this is for **12 cookies**, the cost per cookie is:
\[
\text{Cost per cookie} = \frac{15}{12} = 1.25
\]

- When delivering **18 cookies**, the total charge is **$27.50**. Thus, the cost of the cookies is:
\[
\text{Cost of cookies} = 27.50 - 5 = 22.50
\]
For **18 cookies**, the cost per cookie is:
\[
\text{Cost per cookie} = \frac{22.50}{18} = 1.25
\]

3. **Setting Up the Equation**:
- Now that we know the cost per cookie is **$1.25**, we can express the total charge for delivering **x cookies** as:
\[
y = \text{Total cost} = (\text{Cost per cookie} \times x) + \text{Delivery fee}
\]
- Substituting in the values gives:
\[
y = 1.25x + 5
\]

Thus, the derived equation \( y = 1.25x + 5 \) accurately represents the total charge in dollars for delivering \( x \) cookies.

If you have any doubts or need further clarification about any step, feel free to ask!