Question

Twice as many girls as boys were participating in a tennis tournament. Each pair of players played only one match and there were no draws. The ratio of girl winnings to boy winnings was 5:7.How many players took part in the tournament

Answer 1

twice as many girls as boys.....5 : 7....does that mean there is 12 games ?

Answer 2

I don't think so, it's the ratio of winning girls and boys.

Answer 3

because if there is 12 games, and 5 winning girls that means there is 10 girls, 7 winning boys means 14 boys, and 14 is not twice as 10

Answer 4

what do we have here lads

Answer 5

each pair is this doubles?

Answer 6

need the context haha

Answer 7

well...for every 12 games, girls won 5 and boys won 7.....5/7 of x...but I don't know what x is

Answer 8

each pair of players....so I would say it is doubles

Answer 9

nah i don't think it can be 12 games

Answer 10

would it be affected if it were mixed doubles?

Answer 11

just putting ideas out there

Answer 12

twice as many girls as boys.....2g = 1b.....I have no idea where I am going with this

Answer 13

loool

Answer 14

amistre will get it....just wait

Answer 15

you can just feel it

Answer 16

lol

Answer 17

awkward silence...lol

Answer 18

the bad net, I think so

Answer 19

this sentence is quite ambiguous.. Twice as many girls as boys were participating in a tennis tournament.

did twice as many girls actually PLAY though, or they participated by watching the matches

Answer 20

b g g

b b g g g g

b b b g g g g g g

2:4 is 3 teams
4:8 is 6 teams
6:12 is 9 teams

2n:4n boys to girls is 3n teams to work with at best

Answer 21

bg bg bg bg bg gg gg gg gg gg
^ ^ ^ ^ ^ ^

5 boys win: 5 girls win + 1 more team seems like a bad combination to me
-----------------------------

bb bg bg bg gg gg gg gg gg gg
^ ^ ^ ^ ^ ^

5 boys, 3girl + 4 girls
-----------------------------

bb bb bg gg gg gg gg gg gg gg
^ ^ ^ ^ ^ ^

5 boys, 1girl + 6 girls

the setup of by girl teams doesnt seem to matter if we assume all the boys win

Answer 22

there is 4 players in each game...right...?
so if there was 12 games, then there is 48 players...
am I way off on this ?

Answer 23

assume 2 players in each game - singles

Answer 24

I thought they were doubles

Answer 25

thats what i thought with 48..but not 1:2

Answer 26

bb bb bg bg bg bg gg gg gg gg gg gg
^ ^ ^ ^ ^ ^ +6
5 boys
1girl, need 6 more girls

this seems like a solution

Answer 27

are we sure that boys and girls are mixed

Answer 28

i ran thru a pairing that indicated that the bg matchup had no effect

Answer 29

are we sure that about this !

did twice as many girls actually PLAY though, or they participated by watching the matches!

Answer 30

we shouldnt try to add in extra content ...

Answer 31

so how many players do you think played?

Answer 32

i believe that 8 boys and 16 girls fits for one solution

Answer 33

In a game,
If it is boy VS girl then,
probability of boy win =1/2 and probability of girl win=1/2
If it is girl VS girl then,
probability of girl win =1
If it is boy VS boy then,
probability of boy win =1
Since the number of girls participating is more than the number of boys,
the ratio of girl winning to boy winning can never be less than or equal to 1.

So, either this question makes no sense or I didn't get the question.

Answer 34

"experimental" probability does not conform to "theoritical" probability.

Answer 35

the matches happened already, what we have is the data, we can have the ratio of winning of girls as 1 also. so...

Answer 36

bb bb bg bg bg bg gg gg gg gg gg gg ----> match played
b b b b b g g g g g g g ---> win

Answer 37

then that should fit

Answer 38

i agree :) but im a little biased

Answer 39

does it matter if there is doubles playing ?

Answer 40

well, if 8 boys and 16 girls fits then 8n boys and 16n girls must also fit where n can be any natural number

Answer 41

it doesnt matter for doubles; i assumed doubles when i worked it up

Answer 42

because I figure if there is doubles playing, then there is 4 playersin each game

Answer 43

question says a pair of player plays a game

Answer 44

bb bb bg gg gg gg : win , 5b and 7g
gg gg gg bg bg bg : lose

Answer 45

ohhhhh...I see

Answer 46

Each pair of players played only one match

should we interpret it as "each player played with rest of the players once ?"

Answer 47

so is there 24 people ?

Answer 48

"each player played with rest of the players only once ?"

Answer 49

if so, we need to work it from scratch i would guess

Answer 50

does that mean there is 24 players

Answer 51

i would say that there is a way to solve it no matter what your approach is; just as long as you are consistent in your reasoning/interpretation of the information provided.

Answer 52

the answer is the 9

Answer 53

what you've taken is a simple case which can be worked easily - 12 matches, 24 players
but if we let all combinations with all players it gets nasty

Answer 54

my brain hurts

Answer 55

if n is the number of boys then 2 n is the number of girls
Let N be the total number of matches

Answer 56

using combinatrics we see that \[N=\left(\begin{matrix}3n \\ 2\end{matrix}\right)=\frac{ 3n(3n-1) }{ 2 }\]

Answer 57

N = 3n(3n-1) / 2

or N = 3n/2

?
which interpretation is correct ?

Answer 58

yes 1st one

Answer 59

\[\text{ Let} N_{
gw} \text{be the number of matches won by a girl}\]

Answer 60

Since the ratio between the number of matches won by girls and the number of matches won by boys is 5:7
\[\frac{ N_{gw} }{ N-N_{gw} }=\frac{ 5 }{ 7 } \text{ hence } N_{gw}=\frac{ 5 }{ 12 }N=\frac{ 5 }{ 8 }n(3n-1)\]

Answer 61

The number of matches played between two girls is \[\left(\begin{matrix}2n \\ n\end{matrix}\right)=\frac{ 2n(2n-1) }{ 2 }=n(2n-1)\]

Answer 62

Since in these matches always girls win, we have \[n(2n-1)\le \frac{5}{8}n(3n-1)\]
Solving yields \[n\le 3\]

Further, 8 divides
\[5n(3n−1)\], therefore
n= 3. Thus, there were 9 players.

Answer 63

do you get the solution guys ,cos i kinda get it but not fully ...can any1 expand it?

Answer 64

@amistre64 mention 9 tems somehow and experiment attemted the desired solution ,,,,

Answer 65

qoute of the day
@texaschic101 "my brain hurts"
lol

Answer 66

lol.....

Answer 67

without knowing how the author of the question is defining the win-lose-rematch structure ... and without having the necessary presupposed rules for such a scenario ... i wouldnt know how to verify the results of "9" people in the tournament

Answer 68

but theres no rematch,theres win-loose- and no draws so only win or lose

Answer 69

perhaps you are finding the min num of playes

Answer 70

9 players do not make even match ups, there will be one person waiting to play

how do we determine who the 9th player competes against?

Answer 71

but one ammusing thing is that girls can play against girls

Answer 72

the num of boys should be even so should be twice of it.
if you multiply it by 2, i think it is also solution of the problem.

Answer 73

theres some intricate win-lose-rematch structure if we are to assume a 9 member competition

Answer 74

and by rematch i dont mean 2 people play against each other; but rather there is a re-matching of the players

Answer 75

do you consider the solution above validated and reputable

Answer 76

everyone is playing with everyone else, so how does even or odd matter here

Answer 77

i cant verify the process without knowing how the matching of pairs works in the win-lose structure

p1 <-> p2
p3 <-> p4
p5 <-> p6
p7 <-> p8
p9 <-> [p9?]

Answer 78

seems like one pair meant one player can play more than one matches, i misunderstood it.

Answer 79

okay so i will check how tunnis is played first,but we are not supposed to be tested on games this is a contest question not english and life skills...???
i guess this is not a good question

Answer 80

thanx 4 de effort

Answer 81

No no ... the question is okay, i seem to have presumption abt the question which was not valid. the solution seems fine.

Answer 82

okay so its just the logic...and understanding game structure...wich is not mentioned in the solution!!

Answer 83

is the 5 boys to 7 girls ratio a ratio of different people? or is the same person being counted as a gender win for multiple wins?

Answer 84

except the typo number of matches played between girls is 2nC2

Answer 85

yes i so that

Answer 86

thats why i typed a different solution,above