SOLUTION: Could you please help me work this equation? Translating phrases to algebraic equations: You are choosing between two health clubs. Club A offers membership for a fee of $50 plus

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Question 692027: Could you please help me work this equation?
Translating phrases to algebraic equations:
You are choosing between two health clubs. Club A offers membership for a fee of $50 plus a monthly fee of $25. Club B offers a membership fee of $25 plus a monthly fee of $30.
a. Using variables of your choice, set-up an equation for each club’s membership cost. Make sure your variables are defined clearly.
b. After how many months will the total cost at each health club be the same?
c. What will be the total cost for each club from part (b)?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +C+ = the cost of membership to a health club
of your choice
Let +n+ = the number of months that you belong to a health club
---------------
(a)
Equation for club A:
(1) +C+=+50+%2B+25n+
Equation for club B:
(2) +C+=+25+%2B+30n+
-------------------
(b)
Set the costs equal to eachother
+50+%2B+25n+=+25+%2B+30n+
+30n+-+25n+=+50+-+25+
+5n+=+25+
+n+=+5+
In 5 months the cost to belong to the health clubs be the same
--------------------
(c)
Equation for club A:
(1) +C+=+50+%2B+25n+
(1) +C+=+50+%2B+25%2A5+
(1) +C+=+50+%2B+125+
(1) +C+=+175+
Equation for club B:
(2) +C+=+25+%2B+30n+
(2) +C+=+25+%2B+30%2A5+
(2) +C+=+25+%2B+150+
(2) +C+=+175+
The total cost for both A and B is $175
in 5 months