Brett is joining a new gym. He can join Power Plus or Heavy Hulk. At Power Plus, it will cost $34.20 per month, plus a sign-up fee of $21.00. At Heavy Hulk, it will cost $34.45, plus a sign-up fee of $33.50. Right now, Heavy Hulk is cutting their sign-up fee in half for new members. If Brett signs up at a gym today, after how many months will the cost of the memberships be the same?

Question

A.
17
B.
50
C.
12.25
D.
The cost will never be the same.

Answer 1

To find out after how many months the total cost of memberships at Power Plus and Heavy Hulk will be the same, we can set up equations for the total costs for each gym.

1. Power Plus:

   • Monthly cost: $34.20
   • Sign-up fee: $21.00
   • Total cost after \( m \) months: \[ \text{Cost}_{PP} = 34.20m + 21.00 \]

2. Heavy Hulk:

   • Monthly cost: $34.45
   • Sign-up fee (after halving): \( \frac{33.50}{2} = 16.75 \)
   • Total cost after \( m \) months: \[ \text{Cost}_{HH} = 34.45m + 16.75 \]

Now, we set the total costs equal to each other: \[ 34.20m + 21.00 = 34.45m + 16.75 \]

Next, we will solve for \( m \) by isolating it on one side:

1. Subtract \( 34.20m \) from both sides: \[ 21.00 = 34.45m - 34.20m + 16.75 \] \[ 21.00 = 0.25m + 16.75 \]

2. Subtract \( 16.75 \) from both sides: \[ 21.00 - 16.75 = 0.25m \] \[ 4.25 = 0.25m \]

3. Divide both sides by \( 0.25 \): \[ m = \frac{4.25}{0.25} = 17 \]

Thus, after 17 months, the cost of the memberships at both gyms will be the same.

The correct answer is A. 17.