Pizza Shop Feud

Who has the better price Gino? Or Angelo?

The Pizza Shop Feud!

It was a busy day in the markets of Milan, Italy. And two rival pizza shop owners Angelo and Gino were hard at work in their stores profiting from the large amounts of hungry tourists and people.

At 17:00, John a tourist from America and his family decided they were hungry so they stopped at Gino's pizza shop. " Ah good-a-day sir. My name is-a-Gino. what would you like to order?" John tells Gino he wants a regular (medium) size pizza with 3 toppings. "Ah American! I only sell the normal size pizza in a how-a-do you say? Combo! It is €25.00, and come with 3 toppings on the pizza!"

Menu For Gino's Pizzeria!

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Variables

C= cost in Euros
X= #of pizza bought

The Pizza Shop Feud! (Angelo)

But Gino's prices seemed too expensive to John, so he decided to compare Gino's price with Angelo's Pizzeria across the street. "Welcome! How may I-a-help-a-you?" John explains to Angelo his problem and asks him how much would the same pizza with 3 toppings cost him here at Angelo's Pizzeria. " Well American, at my pizzeria I charge the customer €15.00 plus a fixed fee of €9.75 as a city tax for entering my store and using it's facilities!"

Menu For Angelo's Pizzeria!

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Variables

C= Cost of Pizza
X= # of Pizza ordered

Question's

What Pizzeria do you think John should choose? Why?


When will Angelo's and Gino's pizza cost the same amount? Use the algebraic method and look at the graph to find POI.
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Answers

Equation for Gino

y=mx+b
first we need to calculate the slope using two points from the graph. (1,25) (0,0).

y2-y1/x2-x1
25-0/1-0
25/1
m=25
Y=25x+b
25=25(1)+b
25=25+b
b=25-25
b=0
Y=25x
that is our equation for Gino's Pizzeria.



Equation for Angelo

y=mx+b
first we need to calculate the slope using two points from the graph. (0,9.75) (4,69.75).

y2-y1/x2-x1
69.75-9.75/4-0
60/4
m=15
Y=15x+b
9.75=3.25(0)+b
9.75=0+b
b=9.75-0
b=9.75
b=28-13
b=9.75
y=15x+9.75
that is our equation for Angelo's Pizzeria.



POI Answer

Algebraic Method:
15x+9.75=25x
-10x+9.75=0
-10x= -9.75
x=0.98
now that we found our x value we can substitute it into one of the 2 equations in the beginning to solve for y.

y=25(0.98)
y= 24.50


therefore we have concluded that the POI is approximately (0.98,24.5)

Graphic Method:
For the graphic method we would simply look at the graph and at the point/place where Gino and Angelo's lines intersect that would be our approximate POI. In this case the approximate POI when looking at the graph is (0.98,24.5). Both Gino and Angelo's Pizza's would cost the same if we could buy 0.98 pizza's.
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Summary Statement

Concluding the price analysis of the two Pizzeria's, I found that it would be cheaper in the end for John and his family if they choose Angelo's Pizzeria, because according to my calculations above John would be saving €0.25 for one pizza. Angelo is still a better choice in the long run because the more pizzas are ordered the more savings. In the information example: at Gino's Pizzeria it cost's €50.00 for 2 pizzas, whereas at Angelo's 2 pizzas cost as little as €39.75. This results in a customer saving of €10.25.