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

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.

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