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Nodata
 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?
Nodata
 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?

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akromkhasani
 3 years ago
Best ResponseYou've already chosen the best response.1Let'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

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0I got a different answer. I can't figure out from where did you get the second equation: \[(200  A) + (150  B) = C\]

akromkhasani
 3 years ago
Best ResponseYou've already chosen the best response.1because 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.

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0I think that 200  A represents a part of the people who bought A.

akromkhasani
 3 years ago
Best ResponseYou've already chosen the best response.1no, thats not what i mean. A = people who buy home appliance only then 200A means people who buy home appliance plus car.

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0Then I think it's wrong. But I can't explain it well =(

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0I was trying to solve it using sets theory, but your approach using systems of equations looks very good. This is what I did:

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0Let: \(n(\Omega)\): 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.

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0so \(n(A)\)=200 \(n(B)\) = 150 \(n(C)=n(A\cap B)\) = 25

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0The 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, \(n(B\setminus A) = 150  25=125\)

akromkhasani
 3 years ago
Best ResponseYou've already chosen the best response.1Hmm, I think I misunderstand the problem above. After looking again, I found out that my answer was wrong. The correct one is your answers.

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0and the number of people who bought neither is given by \(n(A\cup B)^C=n(\Omega)n(A\cup B) \)

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0yeah, but you give me insight on another way of solving it!. Thank you much. I will work on that approach.

Nodata
 3 years ago
Best ResponseYou've already chosen the best response.0And I apologize, I think I missplace the question. I haven't noticed that this is the Physics group =P

kropot72
 3 years ago
Best ResponseYou've already chosen the best response.0150  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
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