A gym offers two options for membership plans. Option A includes a one-time fee of $121 and then costs $1 per day. Option B has no initiation fee but costs $12 per
day.
a) Write an equation for the cost of each option.
b) After how many days will the cost of the two options be the same? How
much will both options cost at that time?

Identify variables:
x= # of days
y= total $ amount

Equation:

121+1x=12x

subtract -1x on both sides:

121+1x=12x
-1x -1x

1x-1x cancels out and 12x-1x is 11x so new equation is:

121=11x

now divide 11 on both sides

121 divided by 11 is 11. 11 divided by 11 is 1.

x=11

Now plug x=11 in option A.

121+1(11)=y

121+11=y

132=y

Now plug x=11 to option B.

12(11)= y

132=y

After 11 days the cost of the two options will be the same and both options would cost $132.