jimmy75
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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?

Respuesta :

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

A.

After [tex]15[/tex] months memberships will cost the same.

What is membership ?

Memberships means that you are the member of any specific group.

We have,

Cost of Membership of Alpine Rock-Climbing gym [tex]=\$25[/tex] per month

And, Cost of sign-up fee of Alpine Rock-Climbing gym [tex]=\$125[/tex]

And,

Cost of Membership of  Rocco’s Rock-Climbing gym [tex]=\$30[/tex] per month

And, Cost of sign-up fee of Rocco’s Rock-Climbing gym [tex]=\$50[/tex]

Now,

Let number of months  [tex]=m[/tex]

So,

According to the question;

[tex]125+25m=50+30m[/tex]

⇒ [tex]5m=75[/tex]

[tex]m=15[/tex]

So, After [tex]15[/tex] months memberships will cost the same.

B.

You should join Rocco’s Rock-Climbing gym to pay the least amount of money in a year.

We have,

One year = [tex]12 months[/tex]

So,

Total cost of one year of Alpine Rock-Climbing gym [tex]=125+25m[/tex]

                                                                                       [tex]=125+25*12[/tex]

                                                                                        [tex]=\$425[/tex]

Total cost of one year of Rocco’s Rock-Climbing gym[tex]=50+30m[/tex]

                                                                                         [tex]=50+30*12[/tex]

                                                                                         [tex]=\$410[/tex]

So, Rocco’s Rock-Climbing gym is cheaper than Alpine Rock-Climbing gym.

Hence, we can say that you should join Rocco’s Rock-Climbing gym to pay the least amount of money in a year.

To know more about memberships click here

https://brainly.com/question/352169

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