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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1
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4
Explain how you arrived at your answer.
To find the minimum number of pizzas that could contain pepperoni only, we need to consider the orders made by both Bill and Howard. Since Bill ordered 8 pizzas and Howard ordered 6 pizzas, the total number of pizzas is at least 14.
Now, if every pizza ordered by Howard has sausage (and possibly other toppings), then all the pizzas with pepperoni must come from Bill's order. In this case, the minimum number of pizzas that could contain pepperoni only is 8.
However, if Howard's order contains at least one pizza without sausage (meaning it could have pepperoni only or pepperoni with other toppings), then the minimum number of pizzas with pepperoni only would be less than 8.
Since we are looking for the minimum number, let's assume that Howard's order has exactly one pizza without sausage. In this scenario, the minimum number of pizzas with pepperoni only would be 7 (8 pizzas from Bill's order minus 1 pizza from Howard's order).
Therefore, the minimum number of pizzas that could contain pepperoni only is 7.
Answer: 7