160 people were asked to choose their favourite type of book. They each chose from romance or adventure or horror or thriller. 85 of these people were children. The rest were adult... 160 people were asked to choose their favourite type of book. They each chose from romance or adventure or horror or thriller. 85 of these people were children. The rest were adults. 19 of 33 people who chose romance were children. 34 of 76 people who chose adventure were adults. 7 adults chose thriller. The number of children who chose thriller was the same as the number of adults who chose horror. Work out the total number of people who chose horror. You must show how you get your answer. Read more

Steps to Solve

1. Identify Total Number of Adults First, we determine the total number of adults. Since 160 people were surveyed and 85 of them were children:

$$ \text{Total Adults} = 160 - 85 = 75 $$

2. Determine Children Choosing Romance Next, we note that 19 of the 33 people who chose romance were children. Therefore, the number of adults who chose romance is:

$$ \text{Adults choosing Romance} = 33 - 19 = 14 $$

3. Determine Adults Choosing Adventure From the information given, we know that 34 out of 76 people who chose adventure were adults. Thus, the number of children who chose adventure is:

$$ \text{Children choosing Adventure} = 76 - 34 = 42 $$

4. Determine Adults and Children Choosing Thriller We know 7 adults chose thriller. On the other hand, the number of children who chose thriller is equal to the number of adults who chose horror. Denote the number of children who chose thriller and adults who chose horror by ( x ).

5. Set Up Equation for Total Counts Now we calculate the total number of children and adults for each genre:

• Children: Romance (19) + Adventure (42) + Thriller (x) = 85
• Thus, we can write:

$$ 19 + 42 + x = 85 $$

Simplifying this gives:

$$ x = 85 - 61 = 24 $$

So, 24 children chose thriller.

6. Calculate Adults who Chose Horror Using the same variable ( x ), we know that the number of adults who chose horror is also ( x ). Thus, the number of adults who chose horror is 24.

7. Calculate Total Number of People who Chose Horror Finally, we add the number of children and adults who chose horror:

$$ \text{Total choosing Horror} = \text{Adults choosing Horror} + \text{Children choosing Horror} = 24 + 24 = 48 $$