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?
c >= 2p
p >= 2
10c+15p = 100
see what you can do with that
To maximize the number of pizzas they can order, let's first determine the number of pepperoni pizzas they should order.
Since they must order a minimum of 2 pepperoni pizzas, the options are 2, 3, 4, and so on.
Now, let's find the maximum number of cheese pizzas they can order. They need to order at least twice as many cheese pizzas as the number of pepperoni pizzas.
If they order 2 pepperoni pizzas, they can order 4 cheese pizzas.
If they order 3 pepperoni pizzas, they can order 6 cheese pizzas.
If they order 4 pepperoni pizzas, they can order 8 cheese pizzas.
And so on.
Since they want to order as many pizzas as possible, we should choose the largest possible number of pepperoni pizzas. In this case, they should order 4 pepperoni pizzas.
Now, let's calculate the cost of the pizzas:
4 pepperoni pizzas * $15 per pizza = $60
8 cheese pizzas * $10 per pizza = $80
The total cost of the order is $60 + $80 = $140.
Therefore, based on the given conditions and maximizing the number of pizzas, Mr. Jordan's class can order a maximum of 4 pepperoni pizzas and 8 cheese pizzas, for a total of 12 pizzas.
To find the greatest total number of pizzas that Mr. Jordan's class can order, we need to figure out the maximum number of cheese and pepperoni pizzas they can buy within the given conditions.
Let's assume they buy "p" pepperoni pizzas and "c" cheese pizzas.
According to the problem, they must order at least 2 pepperoni pizzas. So, p ≥ 2.
They also must order at least twice as many cheese pizzas as pepperoni pizzas. So, c ≥ 2p.
Now, let's calculate the maximum number of pizzas they can buy:
Since a pepperoni pizza costs $15, the total cost of all the pepperoni pizzas is given by 15p.
A cheese pizza costs $10, and since they need at least twice as many cheese pizzas as pepperoni pizzas, the minimum number of cheese pizzas they need is 2p. So, the total cost of all the cheese pizzas is 10(2p) = 20p.
The total cost of all the pizzas should not exceed $100, which means the sum of the cost of all the pepperoni pizzas and the cost of all the cheese pizzas should be less than or equal to $100.
So, we can write the following equation:
15p + 20p ≤ 100
Combining like terms, we get:
35p ≤ 100
Dividing both sides by 35, we find:
p ≤ 100/35
p ≤ 20/7
Since the number of pizzas should be a whole number, the maximum value p can take is 2 (since p ≥ 2).
Now that we have the maximum value of p, we can find the corresponding number of cheese pizzas:
c ≥ 2p
c ≥ 2(2)
c ≥ 4
So, the maximum number of pizzas they can order is 2 pepperoni pizzas and 4 cheese pizzas, which totals to 6 pizzas.
Therefore, the greatest total number of pizzas Mr. Jordan’s class can order is 6.