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?
A.
Option 1 only
B.
Option 2 only
C.
Both options 1 and 2
D.
Neither option 1 nor option 2
To determine if the options are viable for Jennifer, we can set up the following equations:
Let x be the number of roller coaster rides and y be the number of other rides.
From Option 1:
5x + 3y = 55 (total tickets)
x + y = 12 (total rides)
From Option 2:
9x + 3y = 55 (total tickets)
x + y = 12 (total rides)
Solving both systems of equations, we find that Option 2 is the only viable option for Jennifer. Therefore, the correct answer is:
B. Option 2 only