Muscle gym offers two different membership plans. each plan includes an initial membership fee plus a monthly charge for a year. the beginner's plan is $10 a month plus an initial fee of $60. the veteran's plan is $15 a month plus an initial fee of $40. nina buys the beginner's plan and joe buys the veteran's plan, both starting in january. in what month has each paid the same total amount to be a member of the gym?

in the 4th month, both amounts would be the same.

Step-by-step explanation:

Let x represent the number of months it will take each of them to pay the same total amount to be a member of the gym.

The Beginner's Plan is $10 a month plus an initial fee of $60. If Nina buys the Beginner's plan, the total amount that she would pay for x months is

10x + 60

The Veteran's Plan is $15 a month plus an initial fee of $40. If Joe buys the Veteran's plan, the total amount that he would pay for x months is

15x + 40

For both amounts to be the same, the number of months would be

15x + 40 = 10x + 60

15x - 10x = 60 - 40

5x = 20

x = 20/5

x = 4