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 if either option is viable for Jennifer, we need to determine if the cost in tickets for each option is less than or equal to the total number of tickets Jennifer has (55) and if the total number of rides is less than or equal to the maximum number of rides Jennifer can take (12).
Option 1:
Number of roller coaster rides = 8
Number of other rides = 5
Total cost in tickets = (8 * 5) + (5 * 3) = 40 + 15 = 55 tickets
Total number of rides = 8 + 5 = 13 rides
Option 2:
Number of roller coaster rides = 9
Number of other rides = 3
Total cost in tickets = (9 * 5) + (3 * 3) = 45 + 9 = 54 tickets
Total number of rides = 9 + 3 = 12 rides
From the calculations, we can see that Option 1 has a total cost in tickets equal to 55 tickets and a total number of rides greater than 12, so it is not viable for Jennifer.
However, Option 2 has a total cost in tickets less than 55 tickets and a total number of rides equal to 12, so it is viable for Jennifer.
Therefore, the answer is:
B. Option 2 only