## No-data 3 years ago In a survey of 500 people, 200 indicated that they would be buying a major appliance within the next month. 150 indicated that they would buy a car, and 25 said that they would purchase both a major appliance and a car. How many will purchase neither. How many will purchase only a car?

1. akromkhasani

Let's define, A = people who buy major appliance only B = people who buy car only C = people who buy both car and major appliance = 25 D = people who buy neither so we get, A + B + C + D = 500 --> A + B + D = 475 (200 - A) + (150 - B) = C --> A + B = 325 solving both equation above D = 150

2. No-data

I got a different answer. I can't figure out from where did you get the second equation: \[(200 - A) + (150 - B) = C\]

3. akromkhasani

because the 200 people is the total people who will buy home appliance, that is people who buy car only and people who buy home appliance plus car, because the 150 people is the total people who will buy car, that is people who buy car only and people who buy car plus home appliance.

4. No-data

I think that 200 - A represents a part of the people who bought A.

5. akromkhasani

no, thats not what i mean. A = people who buy home appliance only then 200-A means people who buy home appliance plus car.

6. No-data

Then I think it's wrong. But I can't explain it well =(

7. No-data

I was trying to solve it using sets theory, but your approach using systems of equations looks very good. This is what I did:

8. No-data

Let: \(n(\Omega)\): Total number of people \(n(A)\): number of people who will buy a major appliance \(n(B)\): number of people who will buy a car \(n(C)\): number of people that will buy both.

9. No-data

so \(n(A)\)=200 \(n(B)\) = 150 \(n(C)=n(A\cap B)\) = 25

10. No-data

The number of people who bought only A is given by: \(n(A\setminus B)=n(A) - n(A\cap B)\) So: \(n(A\setminus B)= 200 - 25=175\) and the number of people who bought only B is given by: \(n(B\setminus A) = n(B)-n(A\cap B)\) or, \(n(B\setminus A) = 150 - 25=125\)

11. akromkhasani

Hmm, I think I misunderstand the problem above. After looking again, I found out that my answer was wrong. The correct one is your answers.

12. No-data

and the number of people who bought neither is given by \(n(A\cup B)^C=n(\Omega)-n(A\cup B) \)

13. No-data

yeah, but you give me insight on another way of solving it!. Thank you much. I will work on that approach.

14. No-data

And I apologize, I think I missplace the question. I haven't noticed that this is the Physics group =P

15. kropot72

150 - 25 = 125 will purchase only a car 200 - 25 = 175 will purchase only a major appliance 25 will purchase both a car and a major appliance. Total number of people making a purchase = 125 + 175 + 25 = 325 Number of people purchasing neither = 500 - 325 = 175