Question

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.(1 point)

Answer 1

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:

1. 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 \( p \times s \).
2. From the calculations, we know that \( p \times s = 40 \).

Now we can summarize our equations:
1. \( p \times s = 40 \)
2. \( p + m = 64 \)

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**.