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 had to chip in 45 cents extra to cover the tab.
HOW MANY PEOPLE WERE IN THE GROUP?
Provide an explanation and a diagram, if necessary.
They split the bill evenly. Three did not pay and that equalled 45cents (.45)
.45/3=.15, so .15x 180 people equals $27.
Mr. Hightower recorded the amount of each project that had been completed at the end of the week. The line plot describes the information he recorded. What fraction of the projects were complete?
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To determine how many people were in the group, we can first subtract the additional amount the remaining people had to chip in from the total bill.
The bill totaled $27 including the tip. Since the remaining people had to chip in an additional 45 cents, we subtract 45 cents from $27 to get $26.55.
Now, if we assume that each person paid the same amount, we can divide $26.55 by the amount each person paid to find the number of people in the group. However, we don't know the exact amount each person paid, so we need to determine the potential values.
Let's assume that each person paid x dollars. In that case, the equation would be:
x * (number of people - 3) + (x + 0.45) * 3 = 26.55
In this equation, "number of people" represents the total number of people in the group.
We can simplify the equation:
x * (number of people - 3) + 3x + 0.45 = 26.55
x * number of people - 3x + 3x + 0.45 = 26.55
x * number of people + 0.45 = 26.55
Now, let's consider the possible values for x that make sense. In this case, we'll assume that x is a multiple of 0.45 since it accounts for the extra amount each person had to pay. Let's start by testing different values for x and see if any of them result in a whole number for the number of people.
If x = 0.45, then the equation becomes 0.45 * number of people + 0.45 = 26.55
This simplifies to 0.45 * number of people = 26.10, which is not a whole number, so it's not a valid solution.
If x = 0.90, then the equation becomes 0.90 * number of people + 0.45 = 26.55
This simplifies to 0.90 * number of people = 26.10, which is still not a whole number.
Let's continue testing values until we find a valid solution.
If x = 1.35, then the equation becomes 1.35 * number of people + 0.45 = 26.55
This simplifies to 1.35 * number of people = 26.10, which is still not a whole number.
If x = 1.80, then the equation becomes 1.80 * number of people + 0.45 = 26.55
This simplifies to 1.80 * number of people = 26.10, which is still not a whole number.
If x = 2.25, then the equation becomes 2.25 * number of people + 0.45 = 26.55
This simplifies to 2.25 * number of people = 26.10, which is still not a whole number.
If x = 2.70, then the equation becomes 2.70 * number of people + 0.45 = 26.55
This simplifies to 2.70 * number of people = 26.10, which is not a whole number.
Finally, if x = 3.15, then the equation becomes 3.15 * number of people + 0.45 = 26.55
This simplifies to 3.15 * number of people = 26.10, which is not a whole number.
Since none of the tested values for x result in a whole number for the number of people, it appears that there is no solution that satisfies the given conditions. It's likely that there was an error in the question or the given information is incomplete.