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.
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?
Let's set up a system of equations to represent the constraints:
Let x be the number of roller coaster rides and y be the number of other rides.
The total number of rides is no more than 12: x + y ≤ 12
The total number of tickets is no more than 55: 5x + 3y ≤ 55
For option 1:
x = 8
y = 5
8 + 5 = 13 > 12, so option 1 is not viable.
For option 2:
x = 9
y = 3
9 + 3 = 12 ≤ 12
5(9) + 3(3) = 45 + 9 = 54 ≤ 55
Option 2 is viable for Jennifer.
Therefore, Jennifer can choose option 2: 9 roller coaster rides and 3 other rides.