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
First, we can set up the following system of inequalities based on the given conditions:
5x + 3y ≤ 55
x + y ≤ 12
For option 1 (8 roller coaster rides and 5 other rides):
5(8) + 3(5) = 40 + 15 = 55
8 + 5 = 13
Since the second inequality is violated, option 1 is not viable for Jennifer.
For option 2 (9 roller coaster rides and 3 other rides):
5(9) + 3(3) = 45 + 9 = 54
9 + 3 = 12
Option 2 satisfies both inequalities, so it is a viable option for Jennifer.
Therefore, the answer is:
B. Option 2 only