Maggie is looking into joining a gym, She went to Axiom Fitness and to Gold's Gym, and they are offering membership plans that work like this:

Axiom: $25 sign-up fee and $30 per month

Gold's: $75 sign-up fee and $25 per month

After how many months will the cost for each gym membership be the same?

Which one will be cheapest in the first few months of membership?

Which one will be the cheapest in the long run?

Axiom: 25 + 30x
Gold’s: 75 + 25x

Set both equations to equal each other.
25 + 30x = 75 + 25x
-25 on both sides
30x = 50 + 25x
-25x on both sides
5x = 50
/5 on both sides
x = 10

Answer to first question:
In 10 months the gym memberships will cost the same.

I substituted 3 in both equations for the ‘first few months.’
25 + 30(3)
25 + 90
115$ with Axiom

75 + 25(3)
75 + 75
150$ with Gold’s

Answer to second question:
Axiom will be cheapest in the first few months of membership.

I substituted 12 in both equations for ‘in the long run.’
25 + 30(12)
25 + 360
385$

75 + 25(12)
75 + 300
375$

Answer to third question:
Gold’s will be the cheapest in the long run.