Question

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. Of of the people ranked vanilla last, of them ranked vanilla before chocolate, and of them ranked vanilla before strawberry, how many people ranked vanilla first?

Answer 1

Answer: 2 people

Step-by-step explanation:

"A poll asked 60 people what their favorite ice cream was between Vanilla, Chocolate, and Strawberry. There were no ties, meaning every person was asked to rank the flavors in order. 3/5 had Vanilla in last place, 1/10 had Vanilla ahead of Chocolate, and 1/3 ranked Vanilla ahead of Strawberry. How many people ranked Vanilla in the first place?"

Total 60 people. No ties.

3/5.60 = 36

1/10.60 = 6

1/3.60 = 20

People could have ranked the 3 flavors like:

     1st place    | 2nd place   | 3rd place

A - Vanilla        | Chocolate  | Strawberry

B - Vanilla        | Strawberry | Chocolate  

C - Chocolate  | Strawberry | Vanilla    

D - Chocolate  | Vanilla        | Strawberry        

E - Strawberry | Chocolate  | Vanilla      

F - Strawberry | Vanilla        | Chocolate        

This way, we have:

• 3/5 had Vanilla in last place = 36

C + E = 36

• 1/10 had Vanilla ahead of Chocolate

A + B + F = 6

• 1/3 ranked Vanilla ahead of Strawberry

A + B + D = 20

We want to know A + B.

Adding all, we have

C + E = 36

A + B + F = 6

A + B + D = 20

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

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

As, we have 60 people and no ties, we know that

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

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

A + B + 60 = 62

A + B = 62 - 60

A + B = 2