Question

Brett is joining a new gym. He can join Power Plus or Heavy Hulk. At Power Plus, it will cost $34.58 per month, plus a sign-up fee of $22.00. At Heavy Hulk, it will cost $34.83, plus a sign-up fee of $34.50. 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?
A.
The cost will never be the same.
B.
50
C.
19
D.
12.25

Answer 1

To solve this problem, we will set up an equation for the total cost of each gym based on the number of months Brett is a member.

Let \( m \) be the number of months.

**Power Plus:**
- Monthly cost: $34.58
- Sign-up fee: $22.00

Total cost for Power Plus after \( m \) months:
\[
\text{Cost}_{PP} = 34.58m + 22
\]

**Heavy Hulk:**
- Monthly cost: $34.83
- Original sign-up fee: $34.50 (now cut in half, so it will be \( 34.50 / 2 = 17.25 \))

Total cost for Heavy Hulk after \( m \) months:
\[
\text{Cost}_{HH} = 34.83m + 17.25
\]

Now, we want to find the number of months \( m \) when the costs are equal:
\[
34.58m + 22 = 34.83m + 17.25
\]

To solve for \( m \), first, rearrange the equation:
\[
34.58m - 34.83m = 17.25 - 22
\]
\[
-0.25m = -4.75
\]

Now, divide both sides by -0.25:
\[
m = \frac{-4.75}{-0.25}
\]
\[
m = 19
\]

Therefore, after 19 months, the cost of the memberships will be the same.

The correct answer is:
**C. 19**