One weekend, there were 98 pizzas ordered for the sophomore dorm. That weekend 19 customers
Ordered their pizza with just pepperoni, 16 customers ordered their pizza with just sausage, 20
Ordered theirs with just onions, 15 ordered theirs with pepperoni and sausage, 9 ordered theirs with
Sausage and onions, 17 ordered theirs with pepperoni and onions, and 2 ordered theirs with all three
Items. How many customers ordered their pizza with pepperoni or sausage (or both)?
A)72
B)35
C)50
D)13

Question

Quizplus · Accepted Answer

To find the number of customers who ordered their pizza with pepperoni or sausage (or both), we add the numbers of customers who ordered pizzas with just pepperoni (19), just sausage (16), both pepperoni and sausage (15), both sausage and onions (9, since some of these will also include those who ordered with pepperoni), both pepperoni and onions (17, since some of these will also include those who ordered with sausage), and all three items (2). However, we must be careful not to double-count the customers who ordered pizzas with both toppings or all three. The correct calculation is: 19 (pepperoni only) + 16 (sausage only) + 15 (pepperoni and sausage) + 2 (all three), since the ones who ordered with both pepperoni and onions or sausage and onions are already included in other categories. This gives us 19 + 16 + 15 + 2 = 52. However, the correct approach to avoid double counting is to first sum all unique combinations and then subtract the overlaps correctly. The initial addition includes overlaps, so the correct method involves using the principle of inclusion-exclusion. The correct total for pepperoni or sausage or both (without double counting) actually involves adding the single ingredient orders (19 + 16), the combinations without considering the all three together since it's counted in the individual combinations, and then correctly accounting for all overlaps, which was not accurately reflected in the initial explanation. The accurate count involves considering all who ordered pepperoni in any combination and all who ordered sausage in any combination, then adding those who ordered both to ensure they are not double-counted. The calculation simplifies to counting each group once: pepperoni only, sausage only, and any combination thereof, including those with onions. The accurate total is derived from understanding that anyone who ordered pepperoni or sausage in any combination should be counted once, leading to the sum of unique orders involving these ingredients.

One Weekend, There Were 98 Pizzas Ordered for the Sophomore