Question

A small social network contains six people who are network friends with six other people in the network, one person who is network friends with five other people in the network, and seven people who are network friends with four other people in the network. The rest are network friends with three other people in the network. The network contains 57pairs of network friends.  How many people are network friends with three other people in the network? Question 5 options: a)  5 b)  51 c)  15 d)  10

Answer 1

C) 15 because there

Answer 2

By setting up an equation using the given numbers of friends and pairs, we deduce that there are 15 people in the network who are friends with three other people.

Step-by-step explanation:

The question asks us to determine how many people in a social network are network friends with three other people in the network, given that there are 57 pairs of network friends in total. We have the following information:

6 people are friends with 6 others,1 person is friends with 5 others,7 people are friends with 4 others,

The rest are friends with 3 others.

Let's denote the number of people who are friends with three others as x. The total number of friendship pairs can be calculated as half the sum of the product of the number of friends each person has, since each friendship is counted twice when considering pairs:

Total Pairs = 1/2 * (6*6 + 1*5 + 7*4 + x*3)

We know the total pairs is 57, so:

57 = 1/2 * (36 + 5 + 28 + 3x)

57 = 1/2 * (69 + 3x)

114 = 69 + 3x

3x = 45

x = 15

Thus, there are 15 people who are network friends with three other people.