a survey of 70 customers was taken at a bookstore regarding the type of books purchased. the survey found that 42 customers purchased mysteries,35 purchased science fiction, 28 purchased romance novels,19 purchased mysteries and sicence fiction, 15 purchased mysteries and romance novels, 11 purchased science fiction and romance novels and 4 purchased all 3 types. how many purchased only romance novels?
You solve this by creating a Venn Diagram with 3 intersecting circles.
Begin by putting the 4 where the 3 circles intersect.
When you are done, add up each part of all of the circles and you should get 70. If you get less than 70 that means customers purchased none of these and the difference between your total and 70 goes out side the circles.
To find the number of customers who purchased only romance novels, we need to subtract the number of customers who purchased romance novels along with other types of books from the total number of customers who purchased romance novels.
Let's break down the information given in the problem:
Number of customers who purchased mysteries = 42
Number of customers who purchased science fiction = 35
Number of customers who purchased romance novels = 28
Number of customers who purchased mysteries and science fiction = 19
Number of customers who purchased mysteries and romance novels = 15
Number of customers who purchased science fiction and romance novels = 11
Number of customers who purchased all three types = 4
To find the number of customers who purchased only romance novels, we can use the principle of inclusion-exclusion.
Step 1: Add up the number of customers who purchased each type individually:
Total number of customers who purchased mysteries = 42
Total number of customers who purchased science fiction = 35
Total number of customers who purchased romance novels = 28
Step 2: Subtract the customers who purchased multiple types of books:
Number of customers who purchased mysteries and science fiction = 19
Number of customers who purchased mysteries and romance novels = 15
Number of customers who purchased science fiction and romance novels = 11
Step 3: Subtract the customers who purchased all three types of books:
Number of customers who purchased all three types = 4
Finally, to find the number of customers who purchased only romance novels, we can calculate as follows:
(28) - (15 + 11 - 4) = 28 - 20 = 8
Therefore, 8 customers purchased only romance novels.