Of 256 consumers polled, some like only thriller movies, some prefer just comedies, and some like both. If 78 people like only thrillers, and 116 like both, how many people prefer only comedies?
Let's assume the number of people who like only thrillers is A, the number of people who like both is B, and the number of people who like only comedies is C.
According to the problem, the total number of consumers polled is 256. Therefore, we can write the equation as:
A + B + C = 256
We also know that 78 people like only thrillers, so we can write:
A = 78
Additionally, we know that 116 people like both thrillers and comedies, which means B = 116.
Substituting the values of A and B into the first equation, we have:
78 + 116 + C = 256
Combining like terms, we get:
194 + C = 256
Finally, we can solve for C by subtracting 194 from both sides of the equation:
C = 256 - 194 = <<256-194=62>>62
Therefore, 62 people prefer only comedies.