You are choosing between two health clubs. Club a offers membership for a fee of 27 plus monthly fee of 19. Club b offers membership for a fee of 17 plus a monthly fee of 21. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
Let the total cost of Club A after x months be represented by the equation:
Total cost of Club A = 27 + 19x
Let the total cost of Club B after x months be represented by the equation:
Total cost of Club B = 17 + 21x
Now, to find when the total costs will be the same, we need to set the two equations equal to each other and solve for x:
27 + 19x = 17 + 21x
10 = 2x
x = 5
Therefore, the total cost for each health club will be the same after 5 months.
To find the total cost at that point, we can substitute x = 5 back into either equation. Let's use the equation for Club A:
Total cost of Club A = 27 + 19(5)
Total cost of Club A = 27 + 95
Total cost of Club A = $122
Therefore, after 5 months, the total cost for Club A will be $122.
Now, let's find the total cost for Club B after 5 months:
Total cost of Club B = 17 + 21(5)
Total cost of Club B = 17 + 105
Total cost of Club B = $122
Therefore, after 5 months, the total cost for Club B will also be $122.