Karen is hosting a pizza party for herself and 29 guests. She wants to order enough pizzas so that each person gets more than 1/5

but less than 2/3 of a pizza. How many different quantities of pizza could Karen order?

Plus Karen herself, there are 30 people eating the pizzas. Since each person gets more than 1/5 of a pizza, there should be more than 30*1/5=6 pizzas. But each gets less than 2/3, so there should be less than 30*2/3=10 pizzas. Therefore, she could order 7, 8, or 9 pizzas, since they are in the range of 6 to 10, exclusive.