Let's analyze the information given about the cookies delivery to derive the correct equation.
We know:
- The delivery fee is constant at $5.
- For 12 cookies, the total charge is $20, which suggests that the cookies cost $15 (since $20 - $5 = $15).
- For 18 cookies, the total charge is $27.50, suggesting the cookies cost $22.50 (since $27.50 - $5 = $22.50).
To find the price per cookie:
- For 12 cookies: $15 ÷ 12 cookies = $1.25 per cookie.
- For 18 cookies: $22.50 ÷ 18 cookies = $1.25 per cookie.
Now, we can establish an equation for the total charge \( y \) for delivering \( x \) cookies. The charge can be calculated as: \[ y = \text{cost of cookies} + \text{delivery fee} \] Where the cost of the cookies is \( 1.25x \) and the delivery fee is \( 5 \): \[ y = 1.25x + 5 \]
Thus, the correct equation representing the total charge in dollars for delivery \( y \) for \( x \) cookies is: \[ y = 1.25x + 5 \]
This corresponds to the first option you provided.