Bill likes pepperoni pizza, and Howard like sausage pizza. Both are willing to eat pizza with sausage and pepperoni both. They order 10 pizzas total, each of which has either sausage or pepperoni and some of which have both. If 6 have pepperoni on them, and 8 have sausage on them, how many pizzas have both sausage and pepperoni on them?

Question

Bill likes pepperoni pizza, and Howard like sausage pizza. Both are willing to eat pizza with sausage and pepperoni both. They order 10 pizzas total, each of which has either sausage or pepperoni and some of which have both. If 6 have pepperoni on them, and 8 have sausage on them, how many pizzas have both sausage and pepperoni on them?

2
4
6
Impossible to tell

Explain your answer.

Answer 1

N(P or S) = N(P) + N(S) - N(P and S)

10 = 6 + 8 - N(P and S)

N(P and S) = 14-10 = 4

You could also do this question by using a Venn diagram.

Answer 2

Thank you, Dr. Reiny!

Answer 3

To find the number of pizzas that have both sausage and pepperoni, we can use the principle of inclusion-exclusion.

We know that there are a total of 10 pizzas, and out of these, 6 have pepperoni and 8 have sausage.

Let's assume that there are x pizzas that have both sausage and pepperoni.

Now, the number of pizzas with pepperoni only is 6 - x (since x pizzas have both, and there are 6 with pepperoni in total).

Similarly, the number of pizzas with only sausage is 8 - x (since x pizzas have both, and there are 8 with sausage in total).

To find the total number of pizzas with either sausage or pepperoni or both, we can add these quantities:

Pizzas with pepperoni + Pizzas with sausage - Pizzas with both = Total pizzas

(6 - x) + (8 - x) - x = 10

Simplifying the equation gives:

6 + 8 - 2x = 10

14 - 2x = 10

-2x = 10 - 14

-2x = -4

x = -4 / -2

x = 2

Therefore, there are 2 pizzas that have both sausage and pepperoni on them.