In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?
8
24
62
86
Explanation
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Using set notation:
y= no. of ppl that like none.
x=3y => no. of ppl that like both Traditional and Modern music, which is equal to 3y(three times y)
MM(Modern Music) =60-3y
TM(Traditional Music) =50-3y
Therefore, 60-3y+3y+50-3y+y=94
collecting like terms; 110-3y+y=94
110-2y=94 =>-2y=-16
y=8
sub. for y in x=3y
x=24
so, the no. of ppl that like only one will be= MM-x + TM-x =60-24 + 50-24 =36 + 26 =62
The explanation is not good at all
A beginner can't understand it
Please let it be in details
Another way of solving it
1. Total members = 94
2. Members who like modern music = 60
3. Members who like traditional music = 50
Let's use the principle of inclusion-exclusion:
Members who like both = x
Members who like only modern = 60 - x
Members who like only traditional = 50 - x
We know that the number of members who like both is three times those who do not like any type of music:
x = 3(94 - 60 - 50 + x)
Simplifying the equation:
x = 3(94 - 110 + x)
x = 3(-16 + x)
x = -48 + 3x
2x = 48
x = 24
Now we know that:
Members who like both = 24
Members who like only modern = 60 - 24 = 36
Members who like only traditional = 50 - 24 = 26
Members who like only one type of music = 36 + 26 = 62
The correct answer is:
C. 62
I think the - in -8 was ignored and I don't know why
Can someone please explain why??
