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 which option(s) are viable for Jennifer, we can set up a system of inequalities based on the given conditions:
Let x be the number of roller coaster rides and y be the number of other rides.
The total number of rides needs to be no more than 12:
x + y ≤ 12
The total number of tickets used needs to be no more than 55:
5x + 3y ≤ 55
Now, we can plug in the values for each option:
Option 1: 8 roller coaster rides and 5 other rides
8 + 5 = 13 (more than 12 rides)
5(8) + 3(5) = 40 + 15 = 55 (exactly 55 tickets used)
Not a viable option.
Option 2: 9 roller coaster rides and 3 other rides
9 + 3 = 12 (exactly 12 rides)
5(9) + 3(3) = 45 + 9 = 54 (less than 55 tickets used)
A viable option.
Therefore, Option 2 only is a viable choice for Jennifer. So the answer is B.