To find the equation that represents the total charge \( y \) for the delivery of \( x \) cookies, we can begin by determining the cost per cookie.
Information given:
- A $5 delivery fee.
- Total cost for 12 cookies: $20.00
- Total cost for 18 cookies: $27.50
Step 1: Find the cost excluding the delivery fee
For 12 cookies: \[ \text{Total cost} = \text{Delivery fee} + (\text{Cost per cookie} \times \text{Number of cookies}) \] \[ 20.00 = 5 + (\text{Cost per cookie} \times 12) \] Subtract the delivery fee from both sides: \[ 20.00 - 5 = \text{Cost per cookie} \times 12 \] \[ 15.00 = \text{Cost per cookie} \times 12 \] Now, divide by 12 to find the cost per cookie: \[ \text{Cost per cookie} = \frac{15.00}{12} = 1.25 \]
For 18 cookies: \[ 27.50 = 5 + (\text{Cost per cookie} \times 18) \] Subtract the delivery fee: \[ 27.50 - 5 = \text{Cost per cookie} \times 18 \] \[ 22.50 = \text{Cost per cookie} \times 18 \] Divide by 18: \[ \text{Cost per cookie} = \frac{22.50}{18} = 1.25 \]
Step 2: Write the equation
Now that we know the cost per cookie is $1.25, we can write the equation for the total charge \( y \): \[ y = 5 + 1.25x \]
Final Equation
Thus, the equation that represents the total charge in dollars \( y \) for the delivery of \( x \) cookies is: \[ y = 5 + 1.25x \]
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