120 people responded to a survey asking which type of vacation they

See attached.

55% ranked B first. That's 66 people. That leaves 54 people who ranked B either second or third. Since we are asked for the number who ranked B third, let's make B3 = x. That means B2 = 54-x.

What does B2 mean? It means that that number of people ranked exactly one of either C or S ahead of B. So 54-x rankings had exactly one of C or S ahead of B.
What does B3 mean? It means that that number of people ranked both C and S ahead of B. If x people ranked both C and S ahead of B, 2x rankings were ahead of B.

25% ranked S>B. That's 30 rankings. 30% ranked C>B. That's 36 rankings.

54-x+2x = 30+36
54+x = 66
x = 12

Answer choice B.

Total respondents: 120.
55% ranked beach holidays (B) first.

Calculate the number of people who ranked B first:
0.55×120=66
Therefore, 66 people ranked B first.

Remaining Respondents:
The remaining respondents did not rank B first:
120−66=54
These 54 people ranked B either second or third.


Define Variables:
Let B3=x represent the number of people who ranked B third.

Consequently,
B2=54−x represents the number of people who ranked B second.
Interpretation of B2 and B3:
B2 means these people ranked exactly one of either city visits (C) or ski trips (S) ahead of B.
B3 means these people ranked both C and S ahead of B. Hence, if x people ranked B third, 2x rankings were ahead of B (one for C and one for S).
Given Percentages:

25% ranked S ahead of B:
0.25×120=30
30% ranked C ahead of B:
0.30×120=36
Formulating the Equation:
Combine the rankings for S and C ahead of B:
30+36=66
Now, the number of people who ranked B second plus twice the number of people who ranked B third should equal 66 (total number of rankings ahead of B):
B2+2x=66
Substitute B2 54−x:
54−𝑥+2𝑥=66
54−x+2x=66
Simplify the equation:
54+x=66
x=66−54
x=12

​

­55% have ranked ski holidays first. So 45% have it ranked 2nd or third.
If people lave ranked ski holidays over beach it can be S,B,C or C,S,B or S,C,B.
If people lave ranked City hikes over beach it can be C,B,S or C,S,B or S,C,B.

Now we can see we have over counted for people ranking beach last as it occurs in the last 2 cases where beach is ranked last. Therefore the extra 10% or 12 people. 

Total who did not rank beach holidays first=People who ranked ski trips ahead of beach holidays+People who ranked city visits ahead of beach holidays−People who ranked both higher.

54 = 30 + 36 - x

x=12

55%*120 =66 --> (120 - 66 = 54 )