I have been trying to figure this out for day's please help if you can.
A survey of 59 customers was taken at a book store regarding the type of novels purchased. The survey found 34 customers purchased mysteries, 27 purchased science fiction, 20 purchased romance novels, 13 purchased mysteries and science fiction, 10 purchased mysteries and romance novels, 7 purchased science fiction and romance novels, and 3 purchased all types.
A) How many purchased mysteries and science fiction, but not romance?
B)How many purchased mysteries or science fiction?
C) How many purchase exactly 2 types?
Just draw a Venn diagram. There are 3 regions, we'll call them m,s,r, with overlapping regions labeled, ms,mr,rs,mrs.
Now start filling them in, from the inside out
mrs = 3
rs = 7-3 = 4
mr = 10-3 = 7
ms = 13-3 = 10
m = 34-(3+7+10) = 21
r = 20-(3+4+7) = 6
s = 27-(3+4+10) = 10
Now you can answer the questions
To solve this problem, we can use a concept called sets and set operations. Let's break down each part of the problem and explain how to get the answer step by step.
A) How many purchased mysteries and science fiction, but not romance?
To answer this question, we need to find the number of customers who purchased both mysteries and science fiction, excluding those who also purchased romance novels.
First, we find the number of customers who purchased mysteries and science fiction together. According to the survey, 13 customers purchased both.
Next, we find the number of customers who purchased mysteries, science fiction, and romance novels. According to the survey, 3 customers purchased all types.
To obtain the number of customers who purchased mysteries and science fiction but not romance, we subtract the number of customers who purchased all types from the number of customers who purchased both mysteries and science fiction: 13 - 3 = 10.
Therefore, 10 customers purchased mysteries and science fiction, but not romance.
B) How many purchased mysteries or science fiction?
To find the number of customers who purchased mysteries or science fiction, we need to combine the number of customers who purchased each type and subtract the number of customers who purchased both.
The number of customers who purchased mysteries is 34, and the number of customers who purchased science fiction is 27.
However, if we add these numbers together (34 + 27 = 61), we would be counting the customers who purchased both twice. So, we need to subtract the number of customers who purchased both from the total.
According to the survey, 13 customers purchased both mysteries and science fiction.
Therefore, the number of customers who purchased mysteries or science fiction is: 34 + 27 - 13 = 48.
Thus, 48 customers purchased mysteries or science fiction.
C) How many purchase exactly 2 types?
To find the number of customers who purchased exactly two types of novels, we need to add up the number of customers who purchased each combination of two types.
According to the survey, there were:
- 13 customers who purchased mysteries and science fiction.
- 10 customers who purchased mysteries and romance.
- 7 customers who purchased science fiction and romance.
- 3 customers who purchased all types.
Adding these numbers together: 13 + 10 + 7 + 3 = 33.
Therefore, 33 customers purchased exactly two types of novels.
I hope this explanation helped you understand the steps to solve the problem. If you have any further questions, feel free to ask!
Let's break down the given information step by step to answer each question.
A)
To find out how many customers purchased mysteries and science fiction, but not romance, we need to subtract the number of customers who purchased all three types (mysteries, science fiction, and romance) from the number of customers who purchased mysteries and science fiction.
From the provided information, we know that 13 customers purchased both mysteries and science fiction, and 3 customers purchased all three types.
Therefore, the number of customers who purchased mysteries and science fiction but not romance is:
13 - 3 = 10
B)
To find out how many customers purchased mysteries or science fiction, we need to add the number of customers who purchased mysteries to the number of customers who purchased science fiction. However, we need to be careful not to count the customers who purchased both types twice.
From the provided information, we know that 34 customers purchased mysteries, 27 purchased science fiction, 13 purchased mysteries and science fiction, and 3 purchased all three types.
Therefore, the number of customers who purchased mysteries or science fiction is:
34 + 27 - 13 + 3 = 51
C)
To find out how many customers purchased exactly 2 types of novels, we need to add the number of customers who purchased exactly two of the three types: (mysteries and science fiction), (mysteries and romance), and (science fiction and romance).
From the provided information, we know that 13 customers purchased mysteries and science fiction, 10 purchased mysteries and romance novels, 7 purchased science fiction and romance novels, and 3 purchased all three types.
Therefore, the number of customers who purchased exactly 2 types is:
13 + 10 + 7 - 3 = 27
To summarize:
A) The number of customers who purchased mysteries and science fiction, but not romance, is 10.
B) The number of customers who purchased mysteries or science fiction is 51.
C) The number of customers who purchased exactly 2 types is 27.