Brett is joining a new gym. He can join Power Plus or Heavy Hulk. At Power Plus, it will cost $34.17 per month, plus a sign-up fee of $21.00. At Heavy Hulk, it will cost $34.42, 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

Let \( x \) be the number of months Brett has a membership.

Cost at Power Plus: \[ \text{Cost}_{\text{Power Plus}} = 21 + 34.17x \]

Cost at Heavy Hulk: The sign-up fee is halved, so it becomes: \[ \text{Cost}_{\text{Heavy Hulk}} = 16.75 + 34.42x \]

We need to find when these costs are equal: \[ 21 + 34.17x = 16.75 + 34.42x \]

Now, simplify this equation: \[ 21 - 16.75 = 34.42x - 34.17x \] \[ 4.25 = 0.25x \]

Now, solve for \( x \): \[ x = \frac{4.25}{0.25} = 17 \]

So, after 17 months, the cost of the memberships will be the same.

Answer: A. 17