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.
x+y < or equal to 12
5x + 3y <or equal to 55
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 options are viable for Jennifer, we need to check if they satisfy both the number of rides and the number of tickets constraints.
Option 1: 8 roller coaster rides and 5 other rides
We need to check if (8+5) ≤ 12 and (5*8 + 3*5) ≤ 55.
This evaluates to 13 ≤ 12, which is false. Therefore, option 1 is not viable.
Option 2: 9 roller coaster rides and 3 other rides
We need to check if (9+3) ≤ 12 and (5*9 + 3*3) ≤ 55.
This evaluates to 12 ≤ 12, which is true, and 48 + 9 ≤ 55, which is also true. Therefore, option 2 is viable.
Therefore, the correct answer is:
B. Option 2 only