A Pizza restaurant offers the following deals"

Deal #1: $8.99 for one large pizza and $5 for each additional large pizza on the same order

Deal#2: $6.00 per large pizza

At what number of pizzas does Deal #1 become a better deal?

What is the cost of 10 pizzas for each deal?

What is the cost per pizza in Deal #1? Which is the better deal and why?

The least number of pizza make deal 1 better than deal 2 is 4

The cost of deal 1 is $53.99 and the cost of deal 2 is $60

The cost per pizza of deal 1 is $5.399

The better deal is deal 1

Step-by-step explanation:

* Deal 1 becomes better if it costs less than deal 2

- Assume that the number of pizza are n

* Deal 1:

∵ The cost of one large pizza = $8.99 for first 1 and = $5 for each

additional one

∵ They ordered n large pizza

∴ The cost = 8.99 + 5 (n - 1)

- Multiply the bracket by 5

∴ The cost = 8.99 + 5n - 5

- Add like terms

∴ The cost = 3.99 + 5n

∴ The cost of deal 1 = 3.99 + 5n

* Deal 2:

∵ The cost of any large pizza is $6

∵ They ordered n large pizza

∴ The cost = 6 * n = 6n

∴ The cost of deal 2 = 6n

- We need Deal 1 better than deal 2

- Then, put the cost of deal 1 < the cost of deal 2

∵ 3.99 + 5n < 6n

- Subtract 5n from both sides

∴ 3.99 < n

∴ n > 3.99

∴ n = 4

* The least number of pizza make deal 1 better than deal 2 is 4

∵ n = 10

∴ The cost of deal 1 = 3.99 + 5 (10) = 53.99

∴ The cost of deal 2 = 6 (10) = 60

* The cost of deal 1 is $53.99 and the cost of deal 2 is $60

∵ The cost per one pizza = total cost : the number of pizza

∴ The cost per pizza of deal 1 = 53.99 : 10 = 5.399

* The cost per pizza of deal 1 is $5.399

∵ The unit price of deal 1 is $5.399

∵ The unit price of deal 2 is $6

∵ $5.399 < $6

∴ The unit rate of deal 1 is less than the unit price of deal 2

* The better deal is deal 1