Question

giving medal for answer help me??


Eight soccer teams are to play each other two times in a season. How many games will be played?
a.
56 games
c.
32 games
b.
16 games
d.
40 games

Answer 1

think of it this way:
you are on a team and your team plays each of the other 7 teams 14 times
each other team plays 14 times as well
so \(8\times 14=112\) then divide by 2 because each game has two teams and get \(112\div 2=56\)

Answer 2

think about it simply like this

team 1 will play teams 2, 3, 4, 5, 6, 7 & 8. that's 7 teams x2 = 14
team 2 will play teams 3, 4, 5, 6, 7, & 8. that's 6 teams x2 =12 (you omit team 1 because they already played against each other 2x)
team 3 will play teams 4, 5, 6, 7, & 8. that's 5 teams x2 = 10
team 4 will play teams 5, 6, 7, & 8. that's 4 teams x2 = 8
team 5 will play teams 6, 7, & 8. that's 3 teams x2 = 6
team 6 will play teams 7 & 8. that's 2 teams x2 = 4
team 7 will play team 8. that's 1 team x2 = 2
team 8 will have already played all their games by now

then add 14 + 12 + 10 + 8 + 6 + 4 + 2 = 56

essentially 8x7 because by the time you get to the last team they've already played all their games.