A group of students went to their favorite restaurant after the football game one Friday night. They all ordered from the menu and forgot to tell the server to give them separate checks. The bill totaled $27, including the tip. They decided to split the bill evenly, and they figured out how much each of them owed. But then three people said they had no money. The rest of the people each had to chip in 45¢ extra to cover the tab. How many people were in the group?
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To solve this problem, let's break it down step by step.
1. We know that the total bill, including the tip, was $27.
2. We also know that the group decided to split the bill evenly, meaning that each person's share would be the same.
3. However, three people in the group said they had no money to contribute, so the rest of the people had to pay extra to cover their portions.
4. The extra amount each person needed to chip in is given as 45¢.
Now, let's set up the equation to solve for the number of people in the group.
Let's assume that there are "x" people in the group who can actually contribute money. These x people each pay an equal share of the bill, which would be (27 - 3 * 0.45)/x (subtracting the amount the three people owe).
Since the rest of the people each had to chip in 45¢ extra, the equation becomes: 27 - (3 * 0.45) + 0.45x = 27.
Simplifying this equation, we have: 27 - 1.35 + 0.45x = 27.
Combining like terms, we get: 0.45x = 1.35.
Dividing both sides by 0.45, we find: x = 3.
Therefore, there were 3 people in the group who could contribute money. To find the total number of people in the group, we need to add the three people who had no money.
Hence, the total number of people in the group is: 3 (contributing people) + 3 (people with no money) = 6.
Therefore, there were 6 people in the group.