Question

Community Gym charges a $70 membership fee and a $60 monthly fee. Workout Gym charges a $210 membership fee and a $50 monthly fee. After how many months will the total amount of money paid to both gyms be the same? What will the amount be?

After months the amount paid to both gyms will be $.

Answer 1

After 14 months, the total amount paid to both Community Gym and Workout Gym will be the same, at $910 each.

Step-by-step explanation:

To determine after how many months the total amount paid to both Community Gym and Workout Gym will be the same, we set up two equations representing the total cost for each gym over time. Let's let x represent the number of months. For Community Gym, the total cost is given by $70 + $60x, and for Workout Gym, it's $210 + $50x.

We set these two expressions equal to find the point where the costs are the same: $70 + $60x = $210 + $50x. Solving for x, we subtract $50x from both sides, getting $70 + $10x = $210. Then, we subtract $70 from both sides to get $10x = $140. Finally, we divide by $10 to find that x equals 14. So, after 14 months, the total cost for both gyms will be the same.

To find out what this total amount will be, we substitute x = 14 back into either gym's total cost equation. Using Community Gym's equation: $70 + $60(14) = $70 + $840 = $910. Therefore, after 14 months, the amount paid to both gyms will be $910.