Please s.b solve this question from SETS section!

[lilisanei]

Can somebody help to solve this question in details?

Among 200 people 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?

Thanks

[limestone]

I have a long approach to the problem. Hope someone will give another more concise solution.

Abbreviation list:
R for rapsberry, S for strawberry, A for apple jam
% Who like only apple jam: A
% who like only apple jam and strawberry : AS
% who like 3 kinds: ASR
% who like both apple and strawberry : AS + ASR ( people that like 3 kinds also like both apple jam and strawberry)

From the given information:
56% = SA+SR+S+SAR
44%=AS+AR+A+ASR
40%=RA+RS+R+RSA
Total 140% = 3SAR + 2SA+2SR+2AR+S+R+A
However 100% = SAR +SA +SR+AR+S+R+A ( all possibility)
Subtract 140% to 100%: 40% = 2SAR + SA+SR+AR
30% =AS+SAR (30% like both apple jam and strawberry)
Subtract 40% to 30%, Then 10% = SAR+SR+AR(note, all elements in this equation have "R", remind me of the equation of people who like R above)
40% = RA+RS+R+RSA
10% =RA+RS+RSA
Subtract 40% to 10%, we have
30% = R
So 30% of all people like ONLY Raspberry. Total no, : 200*30% = 60 people.

[lilisanei]

Thanks lime stone!

Your answer is correct! Good job!
I was looking for a short way. Maybe If I practice more, could follow your solution for other questions!

Thanks again
Leila