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 x is the number of roller coaster rides and y 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 check if the total number of rides and the total number of tickets used in each option satisfy the given conditions.
For Option 1:
Total rides = 8 (roller coaster) + 5 (other) = 13 (which exceeds the maximum allowed rides of 12)
Total tickets used = (8 * 5) + (5 * 3) = 40 + 15 = 55 (which is equal to the maximum allowed tickets of 55)
Option 1 does not satisfy the maximum ride conditions, so it is not viable.
For Option 2:
Total rides = 9 (roller coaster) + 3 (other) = 12 (which is within the maximum allowed rides of 12)
Total tickets used = (9 * 5) + (3 * 3) = 45 + 9 = 54 (which is less than the maximum allowed tickets of 55)
Option 2 satisfies both the maximum ride and maximum ticket conditions, so it is viable.
Therefore, the answer is:
B. Option 2 only