Question

lesson 5 practice problems 1 a restaurant offers delivery for their pizzas for a fee added to the price of the pizzas. one customer pays $25 to have 2 pizzas delivered. another customer pays $58 to have 5 pizzas delivered. how many pizzas are delivered to a customer who paid $80?

Explanation:

Step1: Define variables

Let \( x \) be the number of pizzas and \( y \) be the total cost (in dollars). The cost can be modeled as a linear equation \( y = mx + b \), where \( m \) is the cost per pizza and \( b \) is the delivery fee.

Step2: Set up equations

For the first customer: \( 25 = 2m + b \)
For the second customer: \( 58 = 5m + b \)

Step3: Subtract equations to find \( m \)

Subtract the first equation from the second:
\( 58 - 25 = 5m + b - (2m + b) \)
\( 33 = 3m \)
Solve for \( m \): \( m = \frac{33}{3} = 11 \)

Step4: Find \( b \) using \( m \)

Substitute \( m = 11 \) into \( 25 = 2m + b \):
\( 25 = 2(11) + b \)
\( 25 = 22 + b \)
Solve for \( b \): \( b = 25 - 22 = 3 \)

Step5: Find \( x \) when \( y = 80 \)

Use \( y = 11x + 3 \) and set \( y = 80 \):
\( 80 = 11x + 3 \)
Subtract 3: \( 77 = 11x \)
Solve for \( x \): \( x = \frac{77}{11} = 7 \)

Answer:

7