You are choosing between two health clubs. Club A offers membership for a fee of $ 18 plus a monthly fee of $ 12. Club B offers membership for a fee of $ 16 plus a monthly fee of $ 13. After how many months will the total cost of each health club be the same? What will be the total cost for each club?

The answer to your question is a) 2 months; b) $42.

Step-by-step explanation:

Data

Club A                           Club B

membership = $18        membership = $16

fee  = $12                       fee = $13

Total cost = y

months = x

Process

1.- Write equations to solve this problem

Club A       y = $12x + 18

Club B       y = $13x + 16

2.- Solve the system of equations by equality

                 12x + 18 = 13x + 16

                 12x - 13x = 16 - 18

                          - x = -2

                            x = 2

3.- Conclusion

After 2 months, the cost of both clubs will be the same.

4.- Total cost

Club A           y = 12(2) + 18

                     y = 24 + 18

                     y = $ 42          

Club B           y = $13(2) + 16

                     y = 26 + 16

                     y = $42

The total cost will be $42.

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