A bakery delivers cookies to offices.

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: \[ \boxed{y = 1.25x + 5} \]

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!