Jael went to a restaurant for a buffet dinner with her class. Every 5th person in a group dines for free. It was $18 per person. How many people were there if they paid a total of $378 for dinner?

To solve this problem, we need to determine how many people were in the group if the total payment for the buffet dinner was $378, given that every 5th person dined for free, and the cost for each paying person was $18.

Let's define:
- $ n $ as the total number of people in the group,
- The number of people who paid will be $ \frac{4}{5} $ of the group (since every 5th person dined for free, only 4 out of every 5 people paid).

### Step 1: Set up the equation
The total cost is the number of paying people times the cost per person:
\[
\frac{4}{5} \times n \times 18 = 378
\]

### Step 2: Solve for $ n $
First, simplify the equation:
\[
\frac{4}{5} \times n \times 18 = 378
\]
\[
\frac{72}{5} \times n = 378
\]
Now, multiply both sides by 5 to eliminate the fraction:
\[
72n = 1890
\]
Next, divide both sides by 72:
\[
n = \frac{1890}{72} = 26.25
\]

Since the number of people must be a whole number, we round to the nearest whole number. Therefore, $ n = 25 $.

### Conclusion:
There were 25 people in total.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. If the price per person was $20 instead of $18, how would that affect the total cost?
2. What if every 4th person dined for free? How many people would there be if they paid $378?
3. If the total amount paid was $540, how many people dined in total?
4. What percentage of the group dined for free?
5. How many people would dine for free in a group of 50?

**Tip:** Always cross-check your calculations by substituting the final result back into the original equation.

Solve this algebraic problem where Jael and her group dine at a buffet. Every 5th person dines for free, and the price is $18 per person. Discover how to find the total number of people if the total payment is $378. Perfect for students in Grades 6-8.

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