Question

Jennifer is at an amusement park, where roller coaster rides cost 5 tickets each and all other rides cost 3 tickets each. She has time for no more than 12 rides, and she can use no more than 55 tickets.

The system below represents the above conditions, where  is the number of roller coaster rides and  is the number of other rides.

 x+y is less than or equal to 12

5x+3y is less than or equal to 55

Consider the options below.

Option 1: 8 roller coaster rides and 5 other rides
Option 2: 9 roller coaster rides and 3 other rides
Which option(s), if any, are viable for Jennifer?

Answer 1

Let x = # roller coaster rides and y = # other rides.

Option 1: x = 8, y = 5
- x + y = 8 + 5 = 13, which exceeds 12 → not allowed.
- (Also 5x + 3y = 40 + 15 = 55, meets tickets but fails the time limit.)

Option 2: x = 9, y = 3
- x + y = 9 + 3 = 12 ≤ 12
- 5x + 3y = 45 + 9 = 54 ≤ 55

Only Option 2 is viable.