Of 158 consumers polled, some like only action movies, some prefer just horror movies, and some like both. If 43 people like only action and 62 like both how many people prefer only horror movies? Show your work
Let's denote the number of people who like only action movies as A, the number of people who like only horror movies as H, and the number of people who like both as B.
According to the information given, we know that:
A + B = 43 (Equation 1) - some like only action movies
B = 62 (Equation 2) - some like both
Since some consumers like only action movies and some like both, the number of people who like only horror movies can be calculated by subtracting the total number of people who like only action movies and both from the total number of consumers polled.
Total number of consumers polled = 158
So, A + B + H = 158
We need to solve this equation to find H.
Substituting B from Equation 2 into Equation 1, we have:
A + 62 = 43
Subtracting 62 from both sides:
A = 43 - 62
A = -19
Now, substituting the values we have found for A and B into the equation A + B + H = 158:
-19 + 62 + H = 158
Combining like terms:
43 + H = 158
Subtracting 43 from both sides:
H = 158 - 43
H = 115
Therefore, there are 115 people who prefer only horror movies.