A pizza restaurant, Pizz-A, plans on selling 115 pizzas daily for delivery. For every 15 customers who eat in the restaurant, an additional 4 pizzas will be sold.

Part A: Write an equation to represent the situation. Identify the meaning of all variables used.

Part B: What would an increase in the y-intercept represent?

Part C: Create a second equation for an eat-in only restaurant, in the same chain, with a lower proportion of customers to pizzas sold. Does this equation have the same intercept and slope? Explain your reasoning.

A: y=115+4(n/15) where n is the number of customers. y=115+4n/15
B: An increase in the y intercept would mean the base number of pizzas they sold would be higher. The gradient would remain the same.
C: Say they sold an additional 4 for every 4 customers instead. y=115+4(n/4) y=115+4n/4 The gradient in this case would be 1. I.e. the gradient would be different however the intercept would be the same as they are still selling the same number of pizzas.

Answered by TaylorBayley | 2024-06-10

The **equations **for the additional **pizzas **are solved
What is an Equation?
**Equations **are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation . The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the **equation **be represented as A
Now , the value of A is
Substituting the values in the equation , we get
x be the number of customers who eat in the restaurant
y be the total number of **pizzas **sold
a be the number of pizzas sold for delivery (given as 115)
The equation to represent the situation is:
y = a + b(x/15)
where b is the number of additional pizzas sold for every 15 customers who eat in the restaurant.
This **equation **states that the total number of **pizzas **sold (y) is equal to the number of pizzas sold for delivery (a), plus the number of additional pizzas sold (b) for every 15 customers who eat in the restaurant (x/15).
b)
An increase in the y-intercept would represent an increase in the number of **pizzas **sold for delivery (a). This could happen, for example, if the restaurant increased its marketing efforts to promote delivery orders or lowered the delivery fee to encourage more customers to order for delivery.
c)
Let's assume that the eat-in only restaurant sells **pizzas **at a lower proportion of customers to pizzas sold, with a proportion of 1 pizza sold for every 10 customers who eat in the restaurant. Let:
x be the number of customers who eat in the restaurant
y be the total number of pizzas sold
c be the number of pizzas sold for delivery (still given as 115)
The equation for this situation would be:
y = c + d(x/10)
where d is the number of additional **pizzas **sold for every 10 customers who eat in the restaurant.
This **equation **has a different slope than the previous equation because the proportion of customers to pizzas sold is different. The y-intercept, however, remains the same (c = 115) because it represents the number of pizzas sold for delivery, which is assumed to be the same for both situations.
Hence , the **equations **are solved
To learn more about **equations **click :
https://brainly.com/question/19297665
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Answered by psm22415 | 2024-06-17

The equation representing the pizza sales is y = 115 + 15 4 ​ x , with y as total pizzas sold and x as eat-in customers. An increase in the y-intercept signifies increased delivery sales. The second equation for an eat-in restaurant might be y = 115 + 10 1 ​ x , which has the same intercept but a different slope.
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Answered by psm22415 | 2024-12-26