Question

You have a friendship club. there are 12 members in your club. The 12th day of each month, you have a friendship call. Each member of the club talks to every other member that day by phone. this way everybody expresses his or her friendship with each other. How many conversations are made on that day? Explain
How many conversations occur each year? Show how you figured it out.

If the club adds four new friends, how many conversations will occur each month? Explain your solution.

Suppose another friendship club likes your friendship conversation idea, but wants to know how they can figure out how many conversations will occur given any number of members. Explain how they can figure out the total number of conversations for each month

Answer 1

That day they will have 132 conversations. There are 12 members and each one will be calling the remaining 11 members of the club which means each one will make 11 calls and that will be done by 12 members so 11x12= 132 conversations in total

12 months= 1 year
Every month they make 132 calls so 132x12 will be 1,584 calls per year.

If the club decides to add four new members to the club the conversations each month will rise up to 240.

If the other club likes the idea they can use the following equation
(x-1)(x)
X represents the number of members of the group the subtraction of 1 is when a member makes a call not including them selves so there are 12 members but the one making the call isn't included so there are 11 calls being made then being multiplied by the total number of members.

(x-1)(x)
(12-1)(12)
11(12)
132