Please Help with this Problem

[ace001]

Total Revenue from the sale of adult and student tickets was $180. If twice as many student tickets as adult tickets were sold, and if 27 tickets were sold altogether, what was the total revenue from the sale of student tickets?
(1) The price of each adult ticket was $10
(2) The price of each student ticket was 50% of the price of each adult ticket
The answer is D and I dont understand why each statement alone works.

[albatross86]

First, simplify and translate the question stem:

Total revenue = x*A + y*S = 180 Where x = no.of adults and A = cost per adult; y = no. of students and S = Cost per student.

We also have S = 2*A and A + S = 27
From these 2 we get: A + 2A = 27 => 3A = 27 => A = 9 and S = 18

Thus we have 9x + 18y = 180 OR x + 2y = 20

We need the total revenue from student tickets, i.e = 18*y. Therefore the value of y is sufficient to find our answer.


Statement 1:
x = 10
Substituting in our eqn: 10 + 2y = 20 .... we can find y... SUFFICIENT

Statement 2:
y = 0.5x => x = 2y
Substituting in our eqn: 2y + 2y = 20 ... we can find y.... SUFFICIENT


So you see, simplifying the question stem was really important over here.


Pick D.

[ace001]

Oh wow, thank you SO much! that really helped!