Final answer:
The system of equations for the monthly rate of three different options: Option A, Option B, and Option C, are y = 35 + 12x, y = 115, and y = 100 respectively.
Step-by-step explanation:
In this problem, we need to write a system of equations that represents the monthly rate for three different options: Option A, Option B, and Option C. Let's break down the information given:
Option A: Members pay a $35 membership fee per month and $12 per tanning session. So, the monthly rate for Option A is $35 + $12x, where x represents the number of tanning sessions attended each month.
Option B: Members pay $115 per month for unlimited tanning sessions. So, the monthly rate for Option B is $115.
Option C: Members pay $1,200 per year for unlimited monthly tanning sessions. To convert this to the monthly rate, we divide $1,200 by 12: $1,200 / 12 = $100. So, the monthly rate for Option C is $100.
Therefore, the system of equations that represents the monthly rate for the three options is:
Option A: y = 35 + 12x
Option B: y = 115
Option C: y = 100