A Challenging Question

GMAT Practice Question

At a carnival a patron can purchase an admission ticket plus 20 rides for $29.50 or an admission ticket and 8 rides for $14.50. Assuming the carnival operators price consistently, what is the cost of the admission ticket only?

A)	$1.75
B)	$3.5
C)	$4.5
D)	$6
E)	$7.5

Correct Answer: C

Ticket Cost = (Admission Cost) + (Ride Cost)(Number of Rides)

1. The basic equation for this problem is:
   Ticket Cost = (Admission Cost) + (Ride Cost)(Number of Rides)
2. Let A = the cost of admission
   Let R = the cost per ride
3. Taken together:
   Ticket Cost = A + R(Number of Rides)
4. From the information given, derive two equations:
   29.5 = A + 20R
   14.5 = A + 8R
5. Subtract the lower equation from the upper equation:
   29.5 - 14.5 = A - A + 20R - 8R
   15 = 12R
   R = 15/12 = 5/4
6. Substitute R back into one of the two equations:
   14.5 = A + 8(5/4)
   14.5 = A + 10
   4.5 = A