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?

Question

Aubrey Thomas

Mathematics

31 December, 22:31

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?

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Answers (1)

Know the Answer?

Francesca Hebert · Answer 1

Answer: 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