Thread: Help with formula...(basic algebra)

Formula is N=t^2-t/2

Problem...if a leage has 45 games scheduled, how many teams belong to the league, assumeing that each team plays every team once?

How do you set this problem up??? if "t" is the teams then it seems that we donr have enough info...


The answer for a similar problem but with 36 games is "9 teams".

I just need to see how its done.Can anyone understand this problem?

the total number of games in the league with t matches is 1 + 2 + ... + t-1 = 1 + (t-1) * (t-1)/2 = t*(t-1)/2 = (t^2 - t)/2.

you forgot the parenthesis around t^2 - t... N is the amount of games and t is the amount of teams.

in the case of 9 teams N = (9^2 - 9)/2 = (81 - 9)/2 = 72/2 = 36.

I am sorry but i still didnt understand 36 games = how many teams if it is set up like this then how do you solve it...

36= t^2-t/2....do i need to move 36 to the other side or what?

hmm yea... you have 36 = (t^2 - t)/2 --> (multiply by 2) --> 72 = t^2 - t --> (subtract 72) --> t^2 - t - 72 = 0.
now use the formula to solve the quadratic equation...
for ax^2 + bx + c = 0, x = (-b +- sqrt(b^2 - 4ac))/2a

you'll get two answers, one of which is negative and shouldn't be taken into consideration since you can't have a negative amount of teams.

if N=(t^2-t)/2
then 2N=t^2-t
so 0=t^2-t-2N
factorise to find t
if N=36
then 2*36=t^2-t
0=t^2-t-72
0=(t-9)(t+8)
therefore t=9 or -8
the answer is 9 as -8 does not make physical sense.
For N=45, use same method, i make 10 teams.

It seems like there would be an easier method... is there?
It just seems like the problem itself can be done without using that stupid formula.... thanks for the help...i just have to practice it until i get it i guess.

well you could just try adding 1 + 2 + 3 + ... until you reach the number of games that should be played, then the number of teams is the last number you added + 1.

for example; 36 games... 1 + 2 + ... + 7 + 8 = 36 so the number of teams is 8 + 1 = 9... but that's not the mathematical way to solve it and it would be a little messy when you have like 4851 games to be played (99 teams).

the quadratic formula will help you a lot in the future, try learning it by heart... i haven't used it for years but still remember it