Question

boating club consists of 82 members each member is either a sailboat honour or a Power boat owner if 53 members on on sale boards and 38 members on to powerboats the number of members on both sailboat and the powered boat is​

Answer 1

Given :  boating club consists of 82 members each member is either a sailboat honour or a Power boat owner  

53 members on on sale boards and 38 members on to powerboats

To Find :  the number of members on both sailboat and the powered boat is​

Solution :

sale boards  n(S)  = 53

Power Boat  n(P)  = 38

Total   n(T)  = 82

both    n ( S ∩  P )  = ?

none = 0

 n(T)   =  n(S) +  n(P)  -  n ( S ∩  P )  + none

=> 82 = 53 + 38  -  n ( S ∩  P ) + 0

=> 82 = 91 -  n ( S ∩  P )

=> n ( S ∩  P ) = 9

number of members on both sailboat and the powered boat is​  9

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Answer 2

$Number \: of \: sail \:boat \:owners n(S) = 53$

$Number \:of \: power \: boat \:owners n(P) = 38$

$Number \: of \: boat \: club \:members n( S\cup P) = 82$

$Number \: of \: members \: both$

$sail \:boat \:and \:power \: boat \: n(S\cap P) = ?$

$\boxed{ \pink { n(S\cap P) = n(S) + n(P) - n(S\cup P ) }}$

$= 53 + 38 - 82$

$= 91 - 82$

$= 9$

Therefore.,

$\red{Number \: of \: members \: both}$

$\red{sail \:boat \:and \:power \: boat }\green { = 9}$

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