Membership for the alpine rock-climbing gym costs $25 per month plus a $125 sign-up fee. membership for rocco’s rock-climbing gym costs $30 per month plus a $50 sign-up fee. a. after how many months will the memberships cost the same? b. if you only wanted a one-year membership, which gym would you join to pay the least amount of money?

A.) 125 + 25x = 50 + 30x
Subtract 50 from both sides
75 + 25x = 30x
Subtract 25x from both sides
75 = 5x
Divide 5 from both sides
15 = x
15 months and the memberships would cost the same.

B.) Alpine: 125 + 25x
Rocco: 50 + 30x
Substitute 12 as x to find which is cheaper
ALPINE
125 + 25(12)
125 + 300
425

ROCCO
50 + 30 (12)
50 + 360
410

Rocco is cheaper for one year

This does not make sense