Mr. Jordan’s class is having a pizza party with the $100 they earned in a competition. A cheese pizza costs $10, and a pepperoni pizza costs $15. They must order at least 2 pepperoni pizzas. They also must order at least twice as many cheese pizzas as pepperoni pizzas.
What is the greatest total number of pizzas Mr. Jordan’s class can order
Well, in order to maximize the number of pizzas they can order with their $100, Mr. Jordan's class should definitely go heavy on the cheese!
Let's do some quick math here. Since they have to order at least twice as many cheese pizzas as pepperoni pizzas, we should start with ordering 2 pepperoni pizzas. That's $15 x 2 = $30 gone.
Now, let's see how many cheese pizzas they can afford. They have $100 - $30 = $70 left. Each cheese pizza costs $10, so they can order $70 ÷ $10 = 7 cheese pizzas.
So, in total, they can order 2 pepperoni pizzas and 7 cheese pizzas. That's a grand total of 2 + 7 = 9 pizzas!
Now, maybe they can have a pizza eating contest to see who can eat the most. That way, they can make the most out of their pizza party budget!
To find the greatest total number of pizzas Mr. Jordan's class can order, we need to find the arrangement of pizzas that maximizes the total number of pizzas while staying within the given constraints.
Let's start by determining the maximum number of pepperoni pizzas they can order. Since they need to order at least 2 pepperoni pizzas and each pepperoni pizza costs $15, they can spend a maximum of $100 - (2 * $15) = $70 on cheese pizzas.
Next, let's consider the constraint that they need to order at least twice as many cheese pizzas as pepperoni pizzas. This means that the number of cheese pizzas (C) needs to be at least twice the number of pepperoni pizzas (P), so C ≥ 2P.
Now, let's consider the cost constraint. Each cheese pizza costs $10 and each pepperoni pizza costs $15. We can express the total cost as 10C + 15P, which must not exceed $100.
To find the maximum number of pizzas, we can use trial and error or a systematic approach.
Let's start by assuming they order 2 pepperoni pizzas (P = 2). Since C ≥ 2P, the minimum number of cheese pizzas they would need to order is C = 2 * 2 = 4.
Let's calculate the cost: 10C + 15P = 10 * 4 + 15 * 2 = 40 + 30 = 70.
Since the cost is equal to the maximum amount they can spend on cheese pizzas ($70), this is the optimal solution. They can order 4 cheese pizzas and 2 pepperoni pizzas, which gives a total of 4 + 2 = 6 pizzas.
Therefore, the greatest total number of pizzas Mr. Jordan's class can order is 6.
the answer is 4
don no
10c+15p <= 100
p >= 2
c >= 2p
see what you can do with that