Question

Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she cancels her membership with the first gym after x months and spends the rest of the year, y months, with the second gym. The membership to the first gym costs $75 per month, while the membership for the second gym costs $50 per month. If she ended up spending a total of $825 over the course of the year, how much time did she spend at each gym? Enter a system of equations to represent the situation, then solve the system. The system of equations is . Jan spent months at the first gym and months at the second gym.

Answer 1

Number of months spent in first gym = 9

Number of months spent in second gym = 3

Explanation:

Let she spent x months in a year at first gym and y months in a year at second gym

Now, there are 12 months in one year

⇒ x + y = 12

y = 12 - x .......(1)

Now, total money she spent in one year = $825

⇒ 75·x + 50·y = 825 .........(2)

Putting value of y from equation (1) in equation (2)

75·x + 50·(12 - x) = 825

⇒ 75·x - 50·x + 600 = 825

⇒ 25·x = 225

⇒ x = 9

Now, putting this value of x in equation(1)

⇒ y = 12 - 9

⇒ y = 3

Hence, number of months spent in first gym = 9

And number of months spent in second gym = 3