Let's denote the number of cheese pizzas ordered as \( p \) and the number of mozzarella sticks as \( m \).
We know that there are 8 people total (Ethan and his 7 friends), and they each had 5 slices of pizza. Therefore, the total number of pizza slices consumed by all 8 people is:
\[ 8 \times 5 = 40 \text{ slices} \]
Since there are 64 pieces of food in total, the equation relating the total number of food items can be written as:
\[ p + m = 64 \]
The information given about pizza tells us that:
- Each pizza has a certain number of slices. Let's assume each pizza has \( s \) slices. Therefore, the total number of slices from \( p \) pizzas is \( p \times s \).
- From the calculations, we know that \( p \times s = 40 \).
Now we can summarize our equations:
- \( p \times s = 40 \)
- \( p + m = 64 \)
From the first equation, we can express \( p \) as:
\[ p = \frac{40}{s} \]
Substituting this into the second equation gives:
\[ \frac{40}{s} + m = 64 \]
Solving for \( m \), we rearrange it:
\[ m = 64 - \frac{40}{s} \]
Next, we need to find the values for \( p \) and \( m \) that are integers and make sense for pizza slices. Some reasonable assumptions for \( s \) would be \( 8 \) slices per pizza (which is common).
If \( s = 8 \):
\[ p = \frac{40}{8} = 5 \text{ pizzas} \]
Now substituting \( p \) back into the equation for \( m \):
\[ m = 64 - 5 = 59 \text{ mozzarella sticks} \]
Now we can find out how many mozzarella sticks each person had:
\[ \text{Number of mozzarella sticks per person} = \frac{59}{8} \approx 7.375 \]
Since they can't eat a fraction of a stick, we would round to the nearest whole number, which means: Each person had approximately 7 mozzarella sticks, with a few sticks remaining likely shared.
Therefore, each individual between all 8 consumed about 7 mozzarella sticks.