SOLUTION: Suppose students arrive at school in groups. You are the first to arrive, and you are alone, but still considered a group. The second group to arrive has two more people in it that
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-> SOLUTION: Suppose students arrive at school in groups. You are the first to arrive, and you are alone, but still considered a group. The second group to arrive has two more people in it that
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Question 165396: Suppose students arrive at school in groups. You are the first to arrive, and you are alone, but still considered a group. The second group to arrive has two more people in it that were in your group. The third group of students to arrive has two more people in it than were in the second group. If there are 2250 kids at your school on this day, how many groups will arrive at school, assuming they all meet the requirement of having two more members than the group before them? All groups except the last one must meet the "two more than the last group" requirement. Write an explanation how you got to your answer and write a general statement that would fit this situation no matter how many students were in the school. Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! The first group is one person here is a list of
group numbers and number of people in group. Any
group has 2 more than the previous group
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1 --- 1
2 --- 3
3 --- 5
4 --- 7
5 --- 9
6 --- 11
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Now here is a list of group numbers and total of people so far
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1 --- 1
2 --- 1 + 3 = 4
3 --- 5 + 5 = 9
4 --- 9 + 7 = 16
5 --- 16 + 9 = 25
6 --- 25 + 11 = 36
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Each total is the square of the count number of the group
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etc.
The question then becomes "What group count number squared is under
2250 when the next group count number squared goes over 2250? gives me That's too much gives me still too much gives me
That's under , and
So, people of the 48th group bring the total
up to . So, 48 groups have to arrive at school
(There can be
people in the 48th group)
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For a formula, if = the total number in the school
and = the group count number, = 1,2,3,4.. etc.
The number of groups will be with the
last group having people
