Workout plus offers a membership for $30 each month plus a $100 startup fee. Fit Works offers a membership for $50 each month plus a $20 startup fee. After how many months will memberships to both gyms cost the same amount?

4 months

Step-by-step explanation:

Let

x = number of months

Workout plus = 100 + 30x

Fit works = 20 + 50x

After how many months will memberships to both gyms cost the same amount?

Equate the cost of both gyms

Workout plus = Fit works

100 + 30x = 20 + 50x

100 - 20 = 50x - 30x

80 = 20x

x = 80/20

x = 4 months

After 4 months, memberships to both gyms cost the same amount

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x