a survey taken by 150 people revealed that 65 like apple juice
,and 85 like orange juice. If 40 people like both apple and orange juice, how many people like neither apple nor orange juice?
Let's denote the number of people who only like apple juice as A, the number of people who only like orange juice as B, and the number of people who like both apple and orange juice as C.
From the information given:
A + B + C = total number of people who like apple juice or orange juice
A + C = 65 (people who like apple juice)
B + C = 85 (people who like orange juice)
C = 40 (people who like both apple and orange juice)
Adding the above two equations:
A + B + 2C = 150
A + B + 40 = 150
A + B = 110
Substitute this value back into the total people who like apple juice:
65 = A + C
65 = A + 40
A = 25
Similarly, substitute back this value into the total people who like orange juice:
85 = B + C
85 = B + 40
B = 45
Therefore, the number of people who like neither apple nor orange juice is:
Total number of people - (A + B + C) = 150 - (25 + 45 + 40) = 150 - 110 = 40
So, 40 people like neither apple nor orange juice.