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.
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?
A.
Option 1 only
B.
Option 2 only
C.
Both options 1 and 2
D.
Neither option 1 nor option 2
To determine which option(s) are viable for Jennifer, we can set up inequalities based on the conditions given:
5r + 3o ≤ 55 (total number of tickets)
r + o ≤ 12 (total number of rides)
For Option 1: r = 8, o = 5
5(8) + 3(5) = 40 + 15 = 55 (total number of tickets, which is equal to the limit)
8 + 5 = 13 (total number of rides, which exceeds the limit)
For Option 2: r = 9, o = 3
5(9) + 3(3) = 45 + 9 = 54 (total number of tickets, which is less than the limit)
9 + 3 = 12 (total number of rides, which is equal to the limit)
Therefore, only Option 2 is viable for Jennifer.
The answer is B. Option 2 only.