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in a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. all 60 people responded, and no two flavors were ranked equally by any of the people surveyed. if ​three fifths​ of the people ranked vanilla last, ​one tenth​ of them ranked vanilla before chocolate, and ​one third​ of them ranked vanilla before strawberry, how many people ranked vanilla first?

Respuesta :

The number of people who ranked vanilla first out of total 60 people is 2.

Define the term linear equation?

  • First order equations include linear equations. In the coordinate system, the linear equations is defined for lines.
  • When a homogeneous factor of degree 1 is present in the equation

For the stated question-

Total number of people = 60.

vanilla last: 3/5×60 = 36

vanilla before chocolate: 1/10×60 = 6

vanilla before strawberry: 1/3×60 = 20

Rank of 3 flavours are-

    1st place    | 2nd place   | 3rd place

  1. Vanilla      | Chocolate  | Strawberry
  2. Vanilla       | Strawberry | Chocolate  
  3. Chocolate  | Strawberry | Vanilla    
  4. Chocolate  | Vanilla        | Strawberry        
  5. Strawberry | Chocolate  | Vanilla      
  6. Strawberry | Vanilla        | Chocolate        

Thus,

vanilla last : 3/5 = 36

C + E = 36   ...eq 1

Vanilla ahead of Chocolate -1/10

A + B + F = 6   ...eq 2

Vanilla ahead of Strawberry- 1/3

A + B + D = 20   ...eq 3

Add all three equations-

A + B + F + A + B + D + C + E = 36 + 6 + 20

A + B + A + B + C + D + E + F = 62

60 people with no ties;

A + B + C + D + E + F = 60

A + B + A + B + C + D + E + F = 62

A + B + 60 = 62

A + B = 62 - 60

A + B = 2

Thus, the number of people who ranked vanilla first is 2.

To know more about the linear equation, here

https://brainly.com/question/2030026

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