₦airaland Forum

110 members of a sports club play at least one of the games, football, basketball and volleyball. If 20 play football and basketball only,15 play football and basketball only, 26 play basketball and volleyball only,x play all the three games, 2x each play only one game, how many play basketball altogether

Mike4S:
110 members of a sports club play at least one of
the games, football, basketball and volleyball. If 20
play football and basketball only,15 play football
and basketball only, 26 play basketball and
volleyball only,x play all the three games, 2x each
play only one game, how many play basketball
altogether

How much..

Mike4S:
110 members of a sports club play at least one of
the games, football, basketball and volleyball. If 20
play football and basketball only,15 play football
and basketball only, 26 play basketball and
volleyball only,x play all the three games, 2x each
play only one game, how many play basketball
altogether

you wrote two different values for football and basket ball players.
what about number of football and volleyball players

I guess you wanted to write 20 people played basketball and football only while 15 people played volleyball and football


if I am correct check the picture below to see the solution to the question

Mike4S:
110 members of a sports club play at least one of
the games, football, basketball and volleyball. If 20
play football and basketball only,15 play football
and basketball only, 26 play basketball and
volleyball only,x play all the three games, 2x each
play only one game, how many play basketball
altogether

the answer is below

you can send me a WhatsApp message on so that in case you have any such question to solve l can be of aid to you

matex97:
the answer is below

you can send me a WhatsApp message on so that in case you have any such question to solve l can be of aid to you

my contact is 08168396392

Thanks for the solved Mathematics
I've saved your number for subsequent ones

Mike4S:
Thanks for the solved Mathematics
I've saved your number for subsequent ones

OK you can send me a message now so I can save yours

This question is in the New General Mathematics textbook SS1 by MF Macrae et al. Exerxise 8d No13...
The answer to it is 52 and not 67.
I also got 67 and I am confused... how will I tell my student the answer at the back is not correct?

Akomitipoju:
This question is in the New General Mathematics textbook SS1 by MF Macrae et al. Exerxise 8d No13...
The answer to it is 52 and not 67.
I also got 67 and I am confused... how will I tell my student the answer at the back is not correct?

Rather it's NGM authors that made mistake. The answer is 67 everywhere.
SOLUTION:

Let the Sports Club be denoted by U,
.
F = Football
.
B = Basketball
.
V = Volleyball
.
n(U) = 110
.
n(FnBnC') = 20
.
n(FnVnB') = 15
.
n(BnVnF') = 26
.
n(FnBnV) = x
.
n(FnB'nV') = n(F'nBnV') = (F'nB'nV) = 2x
.
Note: B', F' and V' denote the complements of the various sets(clubs).
.
n(U) = n(FuBuV) + n(FuBuV)'
.
In this case, n(FuBuV)' is empty.
.
110 = 2x + 20 + x + 15 + 2x + 26 + 2x
.
110 = 61 + 7x
.
49 = 7x
.
x = 7
.
n(B) = 20 + 26 + x + 2x
.
n(B) = 20 + 26 + 3x
.
n(B) = 20 + 26 + 21
.
n(B) = 67
.
67 members play Basketball altogether.