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?

Question

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?

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Explain how you arrived at your answer.

Answer 1

To determine the minimum number of pizzas that could contain pepperoni only, we will consider the extremes of the given information.

Let's start by assuming that all of the pizzas ordered by Bill have only pepperoni, and none of the pizzas ordered by Howard have pepperoni. In this scenario, Bill ordered all 8 pizzas with pepperoni, while Howard ordered 0 pizzas with pepperoni. Therefore, the minimum number of pizzas that could contain pepperoni only is 8.

Now, let's consider the opposite scenario. Assuming Bill ordered 0 pizzas with pepperoni, and Howard ordered 6 pizzas with pepperoni. In this case, all 6 pizzas ordered by Howard contain pepperoni only, whereas none of the pizzas ordered by Bill have pepperoni. Thus, the minimum number of pizzas that could contain pepperoni only is 6.

Since we are looking for the minimum number of pizzas that could contain pepperoni only, we take the smaller value between the two scenarios, which is 6. Therefore, the answer is 6.