Question

lesson 5 practice problems
x = number of pizzas y= total cost
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? ______
m=cost per pizza
b= delivery fee
first customer: 25=2m+b
flat rate of $500 for supplies, plus $50 for

Explanation:

Step1: Define linear cost model

Let $x$ = number of pizzas, $y$ = total cost. The model is $y = mx + b$, where $m$ = cost per pizza, $b$ = delivery fee.

Step2: Set up equations from given data

For 2 pizzas: $25 = 2m + b$
For 5 pizzas: $58 = 5m + b$

Step3: Solve for $m$

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

Step4: Solve for $b$

Substitute $m=11$ into $25=2m+b$:
$25 = 2(11) + b$
$25 = 22 + b$
$b = 25 - 22 = 3$

Step5: Find $x$ for $y=80$

Use $y=11x+3$:
$80 = 11x + 3$
$11x = 80 - 3 = 77$
$x = \frac{77}{11} = 8$

Answer:

8 pizzas