At a faculty costume party, each teacher from transylvania Middle School came dressed as his or her favorite creepy creature. The teachers arrived one at a time, and when a new teacher came in, each of the teachers already there lined up at the door and shook hands with the newcomer. Count Dracula(Mr.Blab) kept track of the number of hand shkes exchanged. He said that there were 171 handshakes exchanged at the party.
How many teachers came to the costume party?
The second teacher would have one handshake, the third, two, and so on. Continue on until you get a sum of 171.
I hope this helps. Thanks for asking.
1,333,456,676,766,600
The answer is 19. There were 19 teachers at the party.
I think it is 170 because the second person has the first handshake with the new teacher and its like one less.The answer is 170.
i don't get two methods too solve it
I don't get methods too solve problem heeeeeeeeellllllllllllllllp pllllllllllllease
To solve this problem, we need to find the number of teachers who attended the costume party. Let's assume there were "n" teachers who came to the party.
When the first teacher arrives, there are no other teachers, so no handshakes.
When the second teacher arrives, there is one teacher already there, so there is one handshake.
When the third teacher arrives, there are two teachers already there, so there are two handshakes.
In general, when the "kth" teacher arrives, there are "k-1" teachers already there, and "k-1" handshakes occur.
So, the number of handshakes can be represented as the sum of the first "n-1" positive integers, which can be denoted as:
(1 + 2 + 3 + ... + (n-1))
We know that the sum of the first "m" positive integers can be calculated using the formula:
sum = m * (m + 1) / 2
So, the number of handshakes at the party is:
(n-1) * ((n-1) + 1) / 2 = (n-1) * n / 2
According to the problem, the number of handshakes is given as 171. Thus, we can set up the equation:
(n-1) * n / 2 = 171
Now, we can solve this equation to find the value of 'n'.
n^2 - n - 342 = 0
Using the quadratic formula, we find that the possible values for 'n' are approximately 19.53 and -18.53. Since the number of teachers cannot be negative, we discard the negative value.
So, the number of teachers who came to the costume party is approximately 19.
Therefore, there were about 19 teachers at the costume party.