Expert: Josh - 3/30/2007

Question
Pauline's Piazza Service served 544 pizzas last week. 3/8 of the pizzas served had a mushroom topping. 3/4 0f the mushroom pizzas also had an onion topping. How many pizzas with both mushrooms & onions did the joint serve.

Answer
Hi Myron,

First, note that 1/8 (one eighth) of 544 is 68.
We are told that 3/8 of the 544 pizzas had a mushroom topping.
Number of pizzas with mushroom topping is given by
3*(1/8)*544 = 3*68 = 204

Now concentrate on the 204 mushroom pizzas. Three-quarter of these also had an onion topping. So, we multiply 204 by 3/4 to get 51*3 = 153.

Summary: We multiply the number of pizzas "N" by the fraction with mushroom topping "F(mushroom)", then we multiply this by the fraction with onion topping "F(onion|mushroom)", given that they had a mushroom topping.

Given: N=544, F(mushroom)=3/8, F(onion|mushroom)=3/4

Answer: Pizzas with both mushroom and onion
= N * F(mushroom) * F(onion|mushroom)
= 544 * (3/8) *(3/4)
= 153