# math

posted by .

At the 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 alredy there lined up at the door and shook hands with the newcomer. Count Dracula (Mr. Balb, the math teacher) kept track of the number of handshakes exchanged. He said that there were 171 handshakes exchanged at the party. How many teachers came to the costume party

• math -

Let the number of teachers be n
the number of handshakes of n people is
C(n,2)

so C(n,2) = 171
n!/(2!(n-2)!) = 171
n(n-1) = 342
n^2 - n - 342) = 0
(n-19)(n+18) = 0
n = 19 or n= -18, but n > 0

So 19 teachers came

• math -

People -19
Handshakes- 18
Total handshakes- 171

## Similar Questions

1. ### algebra

Lincoln High School has 98 teachers. Of the 42 female teachers 8 teach math. One-seventh of all teachers teach math. What is the probability that a teacher is a women or teaches math?
2. ### AE.. is this right

In any given multicultural classroom, what are the concerns in terms of social justice for all students?

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 …

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 …
5. ### Probability

A school has 8 math teachers, 6 English teachers, and 2 geography teachers. From this group, a 5 teacher committee is required. Calculate the number of ways that this committee can be formed if at least one geography teachers must …
6. ### Math

A school has four art teachers, three music teachers, and eight history teachers. In how many ways can a student be assigned an art teacher, music teacher, and a history teacher?
7. ### English

1. He went to the teachers' room. There were many teachers, and he was able to see some students scolded by a teacher. 2. The native speaker has his office. In the teacher's office, we talked with the foreign speaker. 3. The teacher's …
8. ### algebra 2

Lincoln High School has 98 teachers. Of the 42 female teachers, 8 teach math. One seventh of all of the teachers teach math. What is the probability that a teacher is a man or does not teach math?
9. ### math

At the faculty costume party , each teacher from Transylvania Middle school came dressed as his of her favorite creepy creature . The teachers arrived one at a time , and when a new teacher came in , each of the teachers already there …
10. ### 7th grade math (probability)

I'm not sure how to answer this: 3. THe 7th grade wants to have a back-up representative just in case the first teacher is absent. Based on the same scenario as #2, if a math teacher was chosen to be the 7th grade representative, what …

More Similar Questions