Ethan had 7 of his friends over. He ordered cheese pizzas and mozzarella sticks for the 8 of them. In all, there were 64 pieces of food. If each person had 5 slices of pizza, find the number of mozzarella sticks each person ate.
To find the number of mozzarella sticks each person ate, we need to first determine the total number of pizza slices. Ethan ordered cheese pizzas for 8 people, and each person had 5 slices. So, the total number of pizza slices is 8 people * 5 slices/person = 40 slices.
Next, we can subtract the number of pizza slices from the total number of food pieces to find the number of mozzarella sticks. There were 64 pieces of food in total, and we know that 40 of them were pizza slices. Therefore, the remaining 64 - 40 = 24 pieces were mozzarella sticks.
Since there were 8 people, we can find the number of mozzarella sticks each person ate by dividing the total number of mozzarella sticks by the number of people. Hence, 24 mozzarella sticks / 8 people = 3 mozzarella sticks per person.
Therefore, each person ate 3 mozzarella sticks.
The seven friends all eat a total of 7 x 5 = <<7*5=35>>35 slices of pizza together.
Ethan therefore ate 35 + 5 = <<35+5=40>>40 mozzarella sticks.
The other 7 friends together ate 64 - 40 = <<64-40=24>>24 mozzarella sticks.
The 7 friends therefore ate 24/7 = <<24/7=3.4285714285714284>>3.4285714285714284 mozzarella sticks each. Answer: \boxed{3}.