To find the equation that represents the total charge in dollars, \( y \), for the delivery of \( x \) cookies, we can start by breaking down the total cost into its components.
The total charge consists of a base delivery fee and a variable cost based on the number of cookies delivered. The delivery fee is given as a fixed amount of 5 dollars.
We have two scenarios provided:
- For 12 cookies, the total charge is 20 dollars.
- For 18 cookies, the total charge is 27.50 dollars.
From these scenarios, we can set up the equations based on the format \( y = mx + b \), where \( m \) is the cost per cookie and \( b \) is the fixed delivery fee.
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For 12 cookies: \[ 20 = m(12) + 5 \] Subtracting 5 from both sides: \[ 15 = 12m \] Solving for \( m \): \[ m = \frac{15}{12} = 1.25 \]
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For 18 cookies: \[ 27.50 = m(18) + 5 \] Subtracting 5 from both sides: \[ 22.50 = 18m \] Solving for \( m \): \[ m = \frac{22.50}{18} = 1.25 \]
Thus, both scenarios yield the same charge per cookie, which is \( 1.25 \).
Now that we have determined \( m = 1.25 \) and the fixed cost \( b = 5 \), we can formulate the final equation:
\[ y = 1.25x + 5 \]
This matches with one of the provided options:
y = 1.25x + 5