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A scientist wants to research the potential spread of germs by contact. She knows that the number of possible handshakes within a group of n people is given by the equation Nequalsone half left parenthesis n squared minus n right parenthesis . Everyone at a party shook hands. There were 171 handshakes in all. How many people attended the? party?

Respuesta :

Cricetus

Answer:

19

Step-by-step explanation:

Here we have to find out number of people attended the party. we are given with the number of the handshakes in the party .

We are going to use the following formula to determine the number of guests

Nos. of handshakes

[tex]H=\frac{1}{2}(n^2-n)[/tex]

Here we have H = 171

Hence our equation becomes

[tex]171=\frac{1}{2}(n^2-n)[/tex]

now we solve it by splitting the middle term method

[tex]171=\frac{1}{2}(n^2-n)\\2*171 =n^2-n\\n^2-n=342\\n^2-n-342=0\\[/tex]

Now we have to find the factors of 342 whose difference to 1. The factors are 19 and 18 in this case. hence we slit our middle term like this

[tex]n^2-n-342=0\\n^2-19n+18n-342=0\\n(n-19)+18(n-19)=0\\(n-19)(n+18)=0\\[/tex]

Hence

either

(x+18)=0 or (x-19) =0 Thus

x=-18 which is not possible as no of people can not be less than 0

x=19 which will our answer

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