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.

y = 1.25x + 5

y = 5x + 1.25

y = 1.25x + 6

y = 5x + 7.50

1 answer

To find the equation that represents the total charge \( y \) for delivering \( x \) cookies, we can use the information provided about the delivery charges.

  1. Identify the total charges:

    • For 12 cookies: Total charge = $20. Therefore, \( (x_1, y_1) = (12, 20) \).
    • For 18 cookies: Total charge = $27.50. Therefore, \( (x_2, y_2) = (18, 27.50) \).
  2. Calculate the delivery cost excluding the delivery fee:

    • The bakery charges a fixed delivery fee of $5, so before considering the delivery fee, the charge for 12 cookies is \( 20 - 5 = 15 \).
    • Similarly, the charge for 18 cookies is \( 27.50 - 5 = 22.50 \).
  3. Determine the cost per cookie:

    • For 12 cookies, the cost per cookie is \( 15/12 = 1.25 \).
    • For 18 cookies, the cost per cookie is \( 22.50/18 = 1.25 \).
  4. Setting up the equation:

    • From the cost per cookie, we can deduce that the cost of cookies is \( 1.25x \).
    • Including the delivery fee, the total charge can be expressed as: \[ y = 1.25x + 5 \]

Thus, the equation that represents the total charge in dollars \( y \) for a delivery of \( x \) cookies is:

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