Final answer:
To find out after how many months the total cost for Health Club A and B is the same, we set up the cost equations for both and solve for the number of months. After setting up the equations CA = 26 + 21.75m and CB = 41 + 14.25m and making them equal to each other, we find that the costs are equal after 2 months.
Step-by-step explanation:
Veronica is comparing the costs of two health clubs to determine after how many months the total cost for each health club will be the same. This question involves creating equations based on the initial membership fee and the monthly fee thereafter for each health club and then finding the point where the costs intersect.
Let's denote the number of months as m. For Health Club A, the total cost CA after m months is CA = 26 + 21.75m (since the membership fee is $26 and the monthly fee is $21.75). For Health Club B, the total cost CB after m months is CB = 41 + 14.25m (where $41 is the membership fee and $14.25 is the monthly fee).
To find out after how many months the two costs will be the same, we set the two equations equal to each other: 26 + 21.75m = 41 + 14.25m.
After simplification, we solve for m:
21.75m - 14.25m = 41 - 26
7.5m = 15
m = 15 / 7.5
m = 2
Therefore, after 2 months, the total cost for both health clubs will be the same.