among 400 students , 51 % study sociology , 46 % study mathematics and 40 % study biology . if 34 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 136 using your analysis : we see that the total number of students who study either maths or sociology = 184 + 204 - 136 = 252 so , in the image we know that the number of students in the zone with the black boundary = 252 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 252 + b + w = 400 or , b + w = 400 - 252 = 148 that is , b = 148 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 148 c
subtract(400, subtract(add(multiply(divide(400, const_100), 51), multiply(divide(400, const_100), 46)), multiply(divide(400, const_100), 34)))