## raimelgarcia5 2 years ago - Students in class are exchanging pencils. 1 student = 0 exchanges 2 students = 2 exchanges 3 students = 6 exchanges 4 students = 12 exchanges how many exhcanges for 7 sutudents? *I know the answer to be: 42 exchanges... but how to get it??? I knwo there is a formula, but I dont knwo how is it and how to use it..* help

1. ParthKohli

1 * 0 = 0 2 * 1 = 2 3 * 2 = 6 4 * 3 = 12 5 * 4 = 20 6 * 5 = 30 7 * 6 = 42

2. raimelgarcia5

yes, thats how i got it... but i know there is a formula... something like an=2n-1+(n-1) or something like that... (not sure if its that one.... and i know how to use that formula... nor i dont kknow what the formula menas.. :/

3. Opcode

Okay. Math in the morning ^_^. There's a pattern. 1 student = 0 exchanges 2 students = 2 exchanges 3 students = 6 exchanges 4 students = 12 exchanges S students = X exchanges S students = X exchanges 7 students = 42 exchanges S = Students X = Exchanges The pattern is how many number of students there is minus one from it then times it by that number. So: S - 1 = Number to multiple by let's call it (N). S * N = X Let's test it: First say there are 10 students. 10 - 1 = 9 10 * 9 = 90 Exchanges. Get it?

4. raimelgarcia5

but why S-1???

5. ParthKohli

Nobody knows...

6. Opcode

Because. The pattern shows that the number multiplied by the students is always one less than it.

7. raimelgarcia5

still dont get it.. (sorry for the persistance..) i wanna learn math like for real..

8. Opcode

So the formula is: (S - 1) = N S * N = X S = Students X = Exchanges N = Number to multiple on "S".

9. Opcode

Say there is: 120 students = ? exchanges Now use the formula: (S - 1) = N S = 120 So (120 - 1) = 119 N = 119 Now for step two: S * N = X We know what S and N are now so plug in the values: 120 * 119 = 14,280 14,280 = X And again: S = Students X = Exchanges N = Number to multiple on "S".

10. raimelgarcia5

yeah.. i get that... i just didnt know why N = S-1 ... but its ok tho... thanks man! :)

11. raimelgarcia5

u are a really good helper :- )

12. Opcode

So the formula is: (S - 1) = N <-- S is for Students (Given) N is for the Number to multiple on "S". IN the pattern to get N. In this case we minus by "1". Then leading us to: S * N = X S = Students X = Exchanges N = Number to multiple on "S". And no problem ^_^.

13. ParthKohli

I am waiting to help like Opcode. :-(

14. Opcode

Help me with what O.o? My stuff is just memorizing things like postulates and theorems. Memory with numbers = Head Ache. (For me at lest).

15. raimelgarcia5

ahah...