Suppose that Bill orders 8 pizzas, each with pepperoni (and possibly other toppings as well), and Howard orders 6 pizzas, each with sausage (and possibly other toppings as well). Without knowing precisely how many pizzas were ordered in total, what is the minimum number of pizzas that could contain pepperoni only?
0
1
2
4
Explain how you arrived at your answer.
Well, let's think about it. Bill ordered 8 pizzas, each with pepperoni, and Howard ordered 6 pizzas, each with sausage. The minimum number of pizzas that could contain pepperoni only would be 0. Why? Because it's possible that all of Bill's pizzas also have sausage toppings, and none of them only have pepperoni. So, the answer is 0, tempting as it may be to imagine a pizza with just a lonely slice of pepperoni sitting there all by itself.
To determine the minimum number of pizzas that could contain pepperoni only, we need to find scenarios in which Bill's pizzas are all pepperoni, while Howard's pizzas have no pepperoni at all.
Since we don't know the total number of pizzas ordered, let's first consider the case where Bill's 8 pizzas and Howard's 6 pizzas are the only pizzas ordered. In this scenario, none of Howard's pizzas have pepperoni, and all of Bill's pizzas have pepperoni. Therefore, the minimum number of pizzas that could contain pepperoni only is 8.
Now, let's consider other scenarios where additional pizzas are added to the order. Regardless of the number of additional pizzas ordered, there will always be at least 8 pizzas that contain pepperoni only (Bill's pizzas). Adding more pizzas will increase the total count, but it would not change the fact that there are at least 8 pizzas with pepperoni only.
Therefore, the minimum number of pizzas that could contain pepperoni only is 8, so the correct answer is 8.
To determine the minimum number of pizzas that could contain pepperoni only, we need to consider the scenario that minimizes the number of pizzas with only pepperoni toppings. In this case, we assume that each pizza ordered by Bill has at least one topping other than pepperoni.
Since Bill ordered 8 pizzas, the minimum number of pizzas that could contain pepperoni only is 0. This means that all 8 pizzas ordered by Bill have toppings other than pepperoni.
To solve this problem, we eliminate the possibility of any pizza having only pepperoni toppings, which ensures the minimum number of pizzas with pepperoni only. Therefore, the correct answer is 0.