One weekend, there were 77 pizzas ordered for the sophomore dorm. That weekend 19 customers ordered onions on their pizza, 15 customers ordered their pizza with just pepperoni, 18 customers ordered...

One weekend, there were 77 pizzas ordered for the sophomore dorm. That weekend 19 customers ordered onions on their pizza, 15 customers ordered their pizza with just pepperoni, 18 customers ordered their pizza with just sausage, 9 ordered theirs with pepperoni and sausage, 8 ordered theirs with sausage and onions, 5 ordered theirs with pepperoni and onions, and 4 ordered theirs with all three items. The remaining pizzas were cheese pizzas with no toppings. How many customers ordered at most two toppings on their pizza? How many customers ordered their pizza with pepperoni or sausage?

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Pizzas are ordered with various combinations of pepperoni, onion and sausage that includes just pepperoni, just sausage, just pepperoni, pepperoni and onion, pepperoni and sausage, sausage and onions, all the three and none of the three.

19 customers ordered onions on their pizza. This includes those with just onion, pepperoni and onion and sausage and onion. 8 ordered theirs with sausage and onions, 5 ordered theirs with pepperoni and onions. The pizzas ordered with just onion is 19 - 8 - 5 = 6. 15 customers ordered their pizza with just pepperoni and 18 customers ordered their pizza with just sausage. The total number of pizzas ordered with just one topping is 6 +15 +18 = 39. 9 ordered theirs with pepperoni and sausage, 8 ordered theirs with sausage and onions, 5 ordered theirs with pepperoni and onions. The total number of pizzas ordered with 2 toppings is 9 + 8 + 5 = 22. 4 pizzas are ordered without any toppings. The number of pizzas ordered with all three toppings is 12.

77 - 12 = 65 customers ordered at most 2 toppings. The number of pizzas ordered with pepperoni or sausage is 15 + 18 + 9 + 8 + 5 + 12 = 67.

65 pizzas were ordered with at most two toppings and 67 of the pizzas ordered had pepperoni or sausage.

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