Membership for the Alpine rock-climbing gym costs $12 per month plus a $120 sign-up fee. Membership for Rocco’s rock-climbing gym costs $20 per month plus a $60 sign-up fee. After how many months will the memberships cost the same?

Around month 7-8

Step-by-step explanation:

Alpiine=

1 month=$132

2=144

3=156

4=168

5=180

6=192

7=204

8=216

9=228

10=240

Rocco=

1 month=80

2=100

3=120

4=140

5=160

6=180

7=200

8=220

9=240

10=260

step-by-step explanation: i dont

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4