Question

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?

Answer 1

Month 4 is when they will pay the same amount

15x+40=10x+60

x=4

Answer 2

Make the Beginner's Plan and the Veteran's Plan equal to each other in an equation.

10m + 60 = 15m + 40

Subtract 10m from both sides.

60 = 5m + 40

Subtract 40 from both sides.

20 = 5m

Divide both sides by 5.

m = 4

Since m = 4, this means in 4 months Nina and Joe will have paid the same total amount to be a member of the gym. They start in January, so 4 months later would be April (counting January because they start in January).

Your answer is m = 4, or
`\boxed {April}`.